How do you solve using the completing the square method x^2+2x-7=17?

May 14, 2017

The solution is $x = 4 \mathmr{and} x = - 6$.

Explanation:

We have:

${x}^{2} + 2 x - 7 = 17$

Adding 8 to both sides completes the square on the left.

${x}^{2} + 2 x + 1 = 25$

Completing squares gives:

${\left(x + 1\right)}^{2} = {5}^{2}$

Taking square roots gives:

$x + 1 = \pm 5$

This gives:

$x = 4 \mathmr{and} x = - 6$

May 14, 2017

{-6;4}
x^2+2x−7=17
$\implies {x}^{2} + 2 x + 1 = 25$
$\implies {\left(x + 1\right)}^{2} = 25$
$\implies x + 1 = 5$ or $x + 1 = - 5$
$\implies x = 4$ or $x = - 6$