Question

How can I factor 5x^2 + 26x - 24 = 0 using the completing the square method.

Answer 1

The answer is -8 with using the completing the square method

Answer 2

QUADRATIC EQUATION

$\mathbb{ANSWER:}$

• $\bold{x = 0.8 \: } \: \sf \: {\color{grey}or} \: \: \: \bold{ x= \frac{4}{5} }$

• $\bold{x = - 6}$

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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.

$\bold{Given \: Equation: \color{brown} 5x²+26x-24=0}$

First, add 24 to both sides.

• $\bold{5x²+26x-24 - \purple{ 24} = 0 + \purple{24}}$

• $\bold{ \implies \: 5x²+26x = 24 }$

Since the coefficient of 5x² is 5, divide both sides by 5.

• $\bold{ \frac{5 {x}^{2} + 26x }{5} = \frac{24}{5} }$

• $\bold{ \implies \: {x}^{2} + \frac{26}{5} x = \frac{24}{5} }$

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.

• $\bold{ {x}^{2} + \frac{26}{5} x + \frac{ \purple{169}}{ \purple{25}}= \frac{24}{5} + \frac{ \purple{169}}{ \purple{25}} }$

• $\bold{ \implies \:\bold{ {x}^{2} + \frac{26}{5} x + \frac{ 169}{ {25}}= \frac{289}{25} } }$

Factor the left side.

• $\bold{(x + \frac{13}{5} ) {}^{2} = \frac{289}{25} }$

Take square root.

• $\bold{x + \frac{13}{5} = ± \: \sqrt{ \frac{289}{25} }}$

Then, add (-13)/5 to both sides.

• $\bold{x + \frac{13}{5} + \frac{\purple{ - 13} }{\purple{ 5}} = \frac{{ - 13} }{{ 5}} ± \: \sqrt{ \frac{289}{25}}}$

• $\bold{ \: x = \frac{ - 13}{5} ± \sqrt{ \frac{289}{25} } }$

• $\implies \: \underline{ \boxed{ \bold{ \frac{4}{5} } \sf \: \: or \: \: \bold{ x = - 6}}}$

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