25(x^2-1)+6=-10 — step-by-step solution

Let's solve in

ℝ

25 \cdot (x^{2} - 1) + 6 = -10

ⓘ We add

10

to both sides

25 \cdot (x^{2} - 1) + 6 + 10 = 0

ⓘ Start from

6

and move forward

10

on the number line:

6 + 10

16

25 \cdot (x^{2} - 1) + 16 = 0

ⓘ Expand by multiplying each term inside the parentheses:

25 \cdot (x^{2} - 1)

25 x^{2} - 25

25 x^{2} - 25 + 16 = 0

ⓘ Start from

-25

and move forward

16

on the number line, getting closer to zero:

- 25 + 16

-9

25 x^{2} - 9 = 0

ⓘ Both sides are divided by

25

x^{2} = \frac{9}{25}

The two numbers whose square is

\frac{9}{25}

are

- \frac{3}{5}

and

\frac{3}{5}

▶Solutions found:

x = {- \frac{3}{5}, \frac{3}{5}}

The numeric value of:

x = {- \frac{3}{5}, \frac{3}{5}}

equals:

▷

x = {-0.6, 0.6}