Solve 3x^2-6=186

$$3 x ^ { 2 } - 6 = 186$$

Solve for x

$$x=8$$

$$x=-8$$

Steps Using Difference of Squares

Subtract 186 from both sides.

$$3x^{2}-6-186=0$$

Subtract 186 from -6 to get -192.

$$3x^{2}-192=0$$

Divide both sides by 3.

$$x^{2}-64=0$$

Consider x^{2}-64. Rewrite x^{2}-64 as x^{2}-8^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-8\right)\left(x+8\right)=0$$

To find equation solutions, solve x-8=0 and x+8=0.

$$x=8 x=-8$$

Steps by Finding Square Root

Add 6 to both sides.

$$3x^{2}=186+6$$

Add 186 and 6 to get 192.

$$3x^{2}=192$$

Divide both sides by 3.

$$x^{2}=\frac{192}{3}$$

Divide 192 by 3 to get 64.

$$x^{2}=64$$

Take the square root of both sides of the equation.

$$x=8 x=-8$$

Steps Using the Quadratic Formula

Subtract 186 from both sides.

$$3x^{2}-6-186=0$$

Subtract 186 from -6 to get -192.

$$3x^{2}-192=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 3 for a, 0 for b, and -192 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 3\left(-192\right)}}{2\times 3}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 3\left(-192\right)}}{2\times 3}$$

Multiply -4 times 3.

$$x=\frac{0±\sqrt{-12\left(-192\right)}}{2\times 3}$$

Multiply -12 times -192.

$$x=\frac{0±\sqrt{2304}}{2\times 3}$$

Take the square root of 2304.

$$x=\frac{0±48}{2\times 3}$$

Multiply 2 times 3.

$$x=\frac{0±48}{6}$$

Now solve the equation x=\frac{0±48}{6} when ± is plus. Divide 48 by 6.

$$x=8$$

Now solve the equation x=\frac{0±48}{6} when ± is minus. Divide -48 by 6.

$$x=-8$$

The equation is now solved.

$$x=8 x=-8$$