Solve 25(x^2-2)+6=-8

$$25 ( x ^ { 2 } - 2 ) + 6 = - 8$$

Solve for x

$$x = \frac{6}{5} = 1\frac{1}{5} = 1.2$$

$$x = -\frac{6}{5} = -1\frac{1}{5} = -1.2$$

Steps Using Difference of Squares

Use the distributive property to multiply 25 by x^{2}-2.

$$25x^{2}-50+6=-8$$

Add -50 and 6 to get -44.

$$25x^{2}-44=-8$$

Add 8 to both sides.

$$25x^{2}-44+8=0$$

Add -44 and 8 to get -36.

$$25x^{2}-36=0$$

Consider 25x^{2}-36. Rewrite 25x^{2}-36 as \left(5x\right)^{2}-6^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(5x-6\right)\left(5x+6\right)=0$$

To find equation solutions, solve 5x-6=0 and 5x+6=0.

$$x=\frac{6}{5} x=-\frac{6}{5}$$

Steps by Finding Square Root

Use the distributive property to multiply 25 by x^{2}-2.

$$25x^{2}-50+6=-8$$

Add -50 and 6 to get -44.

$$25x^{2}-44=-8$$

Add 44 to both sides.

$$25x^{2}=-8+44$$

Add -8 and 44 to get 36.

$$25x^{2}=36$$

Divide both sides by 25.

$$x^{2}=\frac{36}{25}$$

Take the square root of both sides of the equation.

$$x=\frac{6}{5} x=-\frac{6}{5}$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 25 by x^{2}-2.

$$25x^{2}-50+6=-8$$

Add -50 and 6 to get -44.

$$25x^{2}-44=-8$$

Add 8 to both sides.

$$25x^{2}-44+8=0$$

Add -44 and 8 to get -36.

$$25x^{2}-36=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 25 for a, 0 for b, and -36 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 25\left(-36\right)}}{2\times 25}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 25\left(-36\right)}}{2\times 25}$$

Multiply -4 times 25.

$$x=\frac{0±\sqrt{-100\left(-36\right)}}{2\times 25}$$

Multiply -100 times -36.

$$x=\frac{0±\sqrt{3600}}{2\times 25}$$

Take the square root of 3600.

$$x=\frac{0±60}{2\times 25}$$

Multiply 2 times 25.

$$x=\frac{0±60}{50}$$

Now solve the equation x=\frac{0±60}{50} when ± is plus. Reduce the fraction \frac{60}{50} to lowest terms by extracting and canceling out 10.

$$x=\frac{6}{5}$$

Now solve the equation x=\frac{0±60}{50} when ± is minus. Reduce the fraction \frac{-60}{50} to lowest terms by extracting and canceling out 10.

$$x=-\frac{6}{5}$$

The equation is now solved.

$$x=\frac{6}{5} x=-\frac{6}{5}$$