-5(x+6)^2+40=0 — step-by-step solution

1) Let's solve in

ℝ

- 5 \cdot {(x + 6)}^{2} + 40 = 0

ⓘ We subtract

40

from both sides

-5 \cdot {(x + 6)}^{2} = -40

ⓘ Both sides are divided by

-5

{(x + 6)}^{2} = 8

ⓘ The two numbers whose square is

8

are

- 2 \cdot \sqrt{2}

and

2 \cdot \sqrt{2}

x + 6 = - 2 \cdot \sqrt{2}

ⓘ We subtract

6

from both sides

Solution obtained:

x = - 2 \cdot \sqrt{2} - 6

x + 6 = 2 \cdot \sqrt{2}

ⓘ We subtract

6

from both sides

Solution obtained:

x = 2 \cdot \sqrt{2} - 6

▶Solution:

x = {- 2 \cdot \sqrt{2} - 6, 2 \cdot \sqrt{2} - 6}

2) The numeric value of:

x = {- 2 \cdot \sqrt{2} - 6, 2 \cdot \sqrt{2} - 6}

is:

x = {\approx - 2 \cdot 1.4142 - 6, \approx 2 \cdot 1.4142 - 6}

x = {\approx - 2.8284 - 6, \approx 2.8284 - 6}

▷

x = {\approx -8.8284, \approx -3.1716}