How do you solve \x ^ { 2} - 8x = 20?

Jun 2, 2017

$x = - 2 \mathmr{and} x = 10$

Explanation:

${x}^{2} - 8 x = 20$

Re-arrange to form a standard quadratic form
${x}^{2} - 8 x - 20 = 0$

Find the factors of $- 20$ - such as $\left(- 10 \times 2\right)$

where sum of factors = $- 8$ again they are $\left(2 + \left(- 10\right)\right)$

and rearrange in the equation.
${x}^{2} + 2 x - 10 x - 20 = 0$

$x \left(x + 2\right) - 10 \left(x + 2\right) = 0$

$\left(x + 2\right) \left(x - 10\right) = 0$

Setting each factor equal to $0$

$x = - 2 \mathmr{and} x = 10$

Jun 2, 2017

$x = - 2 \text{ or } x = 10$

Explanation:

$\text{rearrange and equate to zero}$

$\Rightarrow {x}^{2} - 8 x - 20 = 0$

$\text{factorise by 'splitting' the middle term}$

$\Rightarrow {x}^{2} + 2 x - 10 x - 20 = 0 \leftarrow \text{ 2x - 10x = -8x}$

$\text{take out a common factor from each 'pair' of terms}$

$\Rightarrow \textcolor{red}{x} \left(x + 2\right) \textcolor{red}{- 10} \left(x + 2\right) = 0$

$\text{take out the common factor of } \left(x + 2\right)$

$\Rightarrow \left(x + 2\right) \left(\textcolor{red}{x - 10}\right) = 0$

$\text{equate each factor to zero and solve}$

$x + 2 = 0 \Rightarrow x = - 2 \leftarrow \text{ solution}$

$x - 10 = 0 \Rightarrow x = 10 \leftarrow \text{ solution}$