Respuesta :
Answer: x = 87.582 , 11.148 .
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Explanation
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Given:
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50 + (x²/20) + (x/20) = 5x ; Solve for "x" ;
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→ First, let us multiply the entire equation (both sides) by "20" ; to get rid of the fractions ;
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20 * {50 + (x²/20) + (x/20) = 5x } ;
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to get:
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1000 + x² + x = 100x ;
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Subtract "x" from each side ;
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1000 + x² + x − x = 100x − x ;
to get: 1000 + x² = 99x ;
Rewrite as:
x² + 1000 = 99x ;
Subtract "99x" from each side of the equation:
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x² + 1000 − 99x = 99x − 99x ;
to get:
x² − 99x + 1000 = 0
This expression is written is "quadratic format" ; that is:
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" ax² + bx + c = 0 ; a ≠ 0 " ;
in which: a = 1 (implied coefficient of "1"; since anything multiplied by "1"; is that same value) ;
b = -99 ;
c = 1000 ;
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→ So, we can solve for "x" using the quadratic equation formula (since the expression cannot be factored):
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x = {- b ± √(b² − 4ac) } / {2a} ;
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Note: - b = - (-99) = 99 ;
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b² = (-99)² = 9801 .
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4ac = 4*a*c = 4*1*1000 = 4000 ;
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(b² − 4ac) = 9801 − 4000 = 5801
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√ (b² − 4ac) = √(5801) = 76.16429609731846
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2a = 2*a = 2*1 = 2
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Rewrite the quadratic formula:
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x = { - b ± √(b² − 4ac) } / {2a} ;
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→ x = (99 ± 76.16429609731846) / 2 ;
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And, with the "±" ; we have 2 (TWO) potential solutions:
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Case 1)
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→ x = (99 + 76.16429609731846) / 2 ;
= (175.16429609731846) / 2
= 87.58214804865923 ; →round to: 87.582 .
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Case 2)
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→ x = (99 − 76.16429609731846) / 2 ;
= (22.83570390268154) / 2 ;
= 11.41785195134077 ; round to: 11.418.
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Answer: x = 87.582 , 11.148 .
_______________________________________________
_______________________________________
Explanation
_________________________________
Given:
_________________________________
50 + (x²/20) + (x/20) = 5x ; Solve for "x" ;
_________________________________
→ First, let us multiply the entire equation (both sides) by "20" ; to get rid of the fractions ;
____________________________________
20 * {50 + (x²/20) + (x/20) = 5x } ;
____________________________________
to get:
____________________________________
1000 + x² + x = 100x ;
____________________________________
Subtract "x" from each side ;
____________________________________
1000 + x² + x − x = 100x − x ;
to get: 1000 + x² = 99x ;
Rewrite as:
x² + 1000 = 99x ;
Subtract "99x" from each side of the equation:
______________________________________
x² + 1000 − 99x = 99x − 99x ;
to get:
x² − 99x + 1000 = 0
This expression is written is "quadratic format" ; that is:
_______________________________________________
" ax² + bx + c = 0 ; a ≠ 0 " ;
in which: a = 1 (implied coefficient of "1"; since anything multiplied by "1"; is that same value) ;
b = -99 ;
c = 1000 ;
____________________________________________________
→ So, we can solve for "x" using the quadratic equation formula (since the expression cannot be factored):
_________________________________________________
x = {- b ± √(b² − 4ac) } / {2a} ;
_____________________________________________________
Note: - b = - (-99) = 99 ;
__________________________________
b² = (-99)² = 9801 .
__________________________________
4ac = 4*a*c = 4*1*1000 = 4000 ;
__________________________________
(b² − 4ac) = 9801 − 4000 = 5801
____________________________________________
√ (b² − 4ac) = √(5801) = 76.16429609731846
____________________________________________
2a = 2*a = 2*1 = 2
____________________________________________
Rewrite the quadratic formula:
____________________________________________
x = { - b ± √(b² − 4ac) } / {2a} ;
____________________________________________
→ x = (99 ± 76.16429609731846) / 2 ;
_____________________________________________
And, with the "±" ; we have 2 (TWO) potential solutions:
_______________________________________________
Case 1)
_______________________________________________
→ x = (99 + 76.16429609731846) / 2 ;
= (175.16429609731846) / 2
= 87.58214804865923 ; →round to: 87.582 .
___________________________________________________
Case 2)
___________________________________________________
→ x = (99 − 76.16429609731846) / 2 ;
= (22.83570390268154) / 2 ;
= 11.41785195134077 ; round to: 11.418.
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Answer: x = 87.582 , 11.148 .
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