QUADRATIC EQUATION
[tex] \mathbb{ANSWER:}[/tex]
- [tex] \bold{x = 0.8 \: } \: \sf \: {\color{grey}or} \: \: \: \bold{ x= \frac{4}{5} } \\ [/tex]
- [tex] \bold{x = - 6}[/tex]
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Step-by-step explanation:
How can we factor 5x^2 + 26x - 24 = 0 using the completing the square method?
Let's solve your equation step-by-step.
[tex] \bold{Given \: Equation: \color{brown} 5x²+26x-24=0}[/tex]
First, add 24 to both sides.
- [tex] \bold{5x²+26x-24 - \purple{ 24} = 0 + \purple{24}}[/tex]
- [tex] \bold{ \implies \: 5x²+26x = 24 }[/tex]
Since the coefficient of 5x² is 5, divide both sides by 5.
- [tex] \bold{ \frac{5 {x}^{2} + 26x }{5} = \frac{24}{5} } \\ [/tex]
- [tex] \bold{ \implies \: {x}^{2} + \frac{26}{5} x = \frac{24}{5} } \\ [/tex]
The coefficient of 26/5x is 26/5. So, let b=26/5.
Then we need to add (b/2)²=169/25 to both sides to complete the square.
Add 169/25 to both sides.
- [tex] \bold{ {x}^{2} + \frac{26}{5} x + \frac{ \purple{169}}{ \purple{25}}= \frac{24}{5} + \frac{ \purple{169}}{ \purple{25}} } \\ [/tex]
- [tex] \bold{ \implies \:\bold{ {x}^{2} + \frac{26}{5} x + \frac{ 169}{ {25}}= \frac{289}{25} } } \\ [/tex]
Factor the left side.
- [tex] \bold{(x + \frac{13}{5} ) {}^{2} = \frac{289}{25} } \\ [/tex]
Take square root.
- [tex] \bold{x + \frac{13}{5} = ± \: \sqrt{ \frac{289}{25} }} \\ [/tex]
Then, add (-13)/5 to both sides.
- [tex] \bold{x + \frac{13}{5} + \frac{\purple{ - 13} }{\purple{ 5}} = \frac{{ - 13} }{{ 5}} ± \: \sqrt{ \frac{289}{25}}} \\ [/tex]
- [tex] \bold{ \: x = \frac{ - 13}{5} ± \sqrt{ \frac{289}{25} } } \\ [/tex]
- [tex] \implies \: \underline{ \boxed{ \bold{ \frac{4}{5} } \sf \: \: or \: \: \bold{ x = - 6}}} \\ [/tex]
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