➷ We can form an equation:
x^2 + x = 90
Subtract 90 from both sides:
x^2 + x - 90 = 0
Now factorize:
(x + 10)(x - 9) = 0
Thus, x = 9 or x = -10
Either of these answers would work, but stick with 9 as your answer.
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ANSWER:
When a number is added to its square the result is 90. The number is 9, -10
SOLUTION:
Let the number be "x"
Given, a number is added to it’s square. This can be represented as,
number + it’s square
[tex]x+x^{2}[/tex]
Also given that, result is 90. Hence the above equation is equal to 90
[tex]\begin{array}{l}{x+x^{2}=90} \\ {x^{2}+x-90=0}\end{array}[/tex]
we can solve this equation by factorizing the equation.
[tex]x^{2}+1 \times x-9 \times 10=0[/tex]
On rewriting the above equation, we get
[tex]\begin{array}{l}{x^{2}+(10-9) \times x-9 \times 10=0} \\ {x^{2}+10 x-9 x-9 \times 10=0}\end{array}[/tex]
Taking “x” as common, we get
x(x + 10) -9(x + 10) = 0
(x + 10)(x – 9) = 0
x+10 = 0, x – 9 = 0
x = -10, 9
Hence, the values of x are 9, -10.
