# How do you solve -4x^2 + x^2 = -36?

Jul 4, 2016

$x = \pm 2 \sqrt{3}$

#### Explanation:

given:$\text{ } \textcolor{g r e e n}{- 4 {x}^{2}} \textcolor{b r o w n}{+ {x}^{2}} = - 36$

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One way of calculating this

We know that$\text{ } + 3 + 1 = + 4$

So " -3-1 = -4

Write $- 4 {x}^{2}$ as $- 3 {x}^{2} - 1 {x}^{2}$

Mathematically should be written as $\textcolor{g r e e n}{- 3 {x}^{2} - {x}^{2}}$
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So we know have:

$\textcolor{g r e e n}{- 3 {x}^{2} - {x}^{2}} \textcolor{b r o w n}{+ {x}^{2}} = - 36$

But $- {x}^{2} + {x}^{2} = 0$ giving

$- 3 {x}^{2} + 0 = - 36$

$- 3 {x}^{2} = - 36$

Divide both sides by $- 3$

$\frac{- 3}{- 3} {x}^{2} = \frac{- 36}{- 3}$

Divide one negative number by another negative number and you have a positive answer.

But $\frac{- 3}{- 3} = + 1 \text{ and } \frac{- 36}{- 3} = + 12$

$1 \times {x}^{2} = 12$

${x}^{2} = 12$

Square root both sides

$\sqrt{{x}^{2}} = \sqrt{3 \times {2}^{2}}$

$x = \pm 2 \sqrt{3}$