# How do you solve 5(x-7)^2=135?

Jun 5, 2017

12.2 & 1.8

#### Explanation:

Given, $5 {\left(x - 7\right)}^{2} = 135$

$\Rightarrow {x}^{2} - 14 x + 49 = \frac{135}{5}$

$\Rightarrow {x}^{2} - 14 x + 49 - 27 = 0$

$\Rightarrow {x}^{2} - 14 x + 22 = 0$

$\Rightarrow x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$ [here b = -14, c=22 & a = 1]

$\Rightarrow x = \frac{- \left(- 14\right) \pm \sqrt{{\left(- 14\right)}^{2} - 4 \cdot 1 \cdot 22}}{2 \cdot 1}$

$\Rightarrow x = \frac{14 \pm \sqrt{196 - 88}}{2}$

$\Rightarrow x = \frac{14 \pm \sqrt{108}}{2}$

$\Rightarrow x = \frac{14 \pm 10.4}{2}$

$\Rightarrow x = \frac{14 + 10.4}{2} , \frac{14 - 10.4}{2}$

$\Rightarrow x = 12.2 , 1.8$

Jun 5, 2017

$x = 12.196 \mathmr{and} x = 1.804$

#### Explanation:

Isolate the bracket that contains the $x$ by dividing both sides by $5$

$\frac{5 {\left(- 7\right)}^{2}}{5} = \frac{135}{5}$

${\left(x - 7\right)}^{2} = 27$

Find the square root of both sides:

$x - 7 = \pm \sqrt{27}$

Solve using the positive and negative roots:

$x = + \sqrt{27} + 7 = 12.196$

$x = - \sqrt{27} + 7 = 1.804$