x^2+12x+36=7 — step-by-step solution | Explain MAths

x^2+12x+36=7

Let's solve in

ℝ

:

x^{2} + 12 x + 36 = 7

We recognize a special product:

x^{2} + 12 x + 36

=

{(x + 6)}^{2}

{(x + 6)}^{2} = 7

ⓘ The two numbers whose square is

7

are

- \sqrt{7}

and

\sqrt{7}

x + 6 = - \sqrt{7}

ⓘ We subtract

6

from both sides

Solution found:

x = - \sqrt{7} - 6

x + 6 = \sqrt{7}

ⓘ We subtract

6

from both sides

Solution found:

x = \sqrt{7} - 6

▶Solution:

x = {- \sqrt{7} - 6, \sqrt{7} - 6}

The numeric value of:

x = {- \sqrt{7} - 6, \sqrt{7} - 6}

equals:

x = {\approx - 2.6458 - 6, \approx 2.6458 - 6}

▷

x = {\approx -8.6458, \approx -3.3542}