(5x+7)^2=3 — step-by-step solution

1) Let's solve in

ℝ

{(5 x + 7)}^{2} = 3

ⓘ The two numbers whose square is

3

are

- \sqrt{3}

and

\sqrt{3}

5 x + 7 = - \sqrt{3}

ⓘ We subtract

7

from both sides

5 x = - \sqrt{3} - 7

ⓘ Both sides are divided by

5

x = \frac{- \sqrt{3} - 7}{5}

ⓘ The minus sign is factored out, changing the sign of each term:

- \sqrt{3} - 7

- (\sqrt{3} + 7)

x = - \frac{\sqrt{3} + 7}{5}

Solution found:

x = - \frac{7 + \sqrt{3}}{5}

5 x + 7 = \sqrt{3}

ⓘ We subtract

7

from both sides

5 x = \sqrt{3} - 7

ⓘ Both sides are divided by

5

Solution obtained:

x = \frac{\sqrt{3} - 7}{5}

▶Solution:

x = {- \frac{7 + \sqrt{3}}{5}, \frac{\sqrt{3} - 7}{5}}

2) The numeric value of:

x = {- \frac{7 + \sqrt{3}}{5}, \frac{\sqrt{3} - 7}{5}}

equals:

x = {\approx - \frac{7 + 1.7321}{5}, \approx \frac{1.7321 - 7}{5}}

x = {\approx - \frac{8.7321}{5}, \approx - \frac{5.2679}{5}}

▷

x = {\approx -1.7464, \approx -1.0536}