x^2+(-2/7)^2=1 — step-by-step solution

1) Let's solve in

ℝ

x^{2} + {(- \frac{2}{7})}^{2} = 1

ⓘ We subtract

{(- \frac{2}{7})}^{2}

from both sides

x^{2} = 1 - {(- \frac{2}{7})}^{2}

ⓘ The power of a quotient is the quotient of the powers, (a/b)^n = a^n/b^n:

{(- \frac{2}{7})}^{2}

\frac{{(-2)}^{2}}{7^{2}}

x^{2} = 1 - \frac{{(-2)}^{2}}{7^{2}}

ⓘ Powers are computed before multiplications, additions and subtractions. An integer power is a repeated product:

{(-2)}^{2}

(-2) \cdot (-2)

4

7^{2}

7 \cdot 7

49

x^{2} = 1 - \frac{4}{49}

ⓘ To add fractions, put them over the same denominator, then add the numerators:

1 - \frac{4}{49}

\frac{49 - 4}{49}

x^{2} = \frac{49 - 4}{49}

ⓘ The numerator and the denominator are computed before the division:

49 - 4

45

x^{2} = \frac{45}{49}

The two numbers whose square is

\frac{45}{49}

are

- \frac{3 \cdot \sqrt{5}}{7}

and

\frac{3 \cdot \sqrt{5}}{7}

▶Solutions obtained:

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

2) The numeric value of:

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

equals:

x = {\approx - \frac{3 \cdot 2.2361}{7}, \approx \frac{3 \cdot 2.2361}{7}}

x = {\approx - \frac{6.7082}{7}, \approx \frac{6.7082}{7}}

▷

x = {\approx -0.9583, \approx 0.9583}