Solve 4x^2-10=186

$$4 x ^ { 2 } - 10 = 186$$

Solve for x

$$x=7$$

$$x=-7$$

Steps Using Difference of Squares

Subtract 186 from both sides.

$$4x^{2}-10-186=0$$

Subtract 186 from -10 to get -196.

$$4x^{2}-196=0$$

Divide both sides by 4.

$$x^{2}-49=0$$

Consider x^{2}-49. Rewrite x^{2}-49 as x^{2}-7^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-7\right)\left(x+7\right)=0$$

To find equation solutions, solve x-7=0 and x+7=0.

$$x=7 x=-7$$

Steps by Finding Square Root

Add 10 to both sides.

$$4x^{2}=186+10$$

Add 186 and 10 to get 196.

$$4x^{2}=196$$

Divide both sides by 4.

$$x^{2}=\frac{196}{4}$$

Divide 196 by 4 to get 49.

$$x^{2}=49$$

Take the square root of both sides of the equation.

$$x=7 x=-7$$

Steps Using the Quadratic Formula

Subtract 186 from both sides.

$$4x^{2}-10-186=0$$

Subtract 186 from -10 to get -196.

$$4x^{2}-196=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -196 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-196\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-196\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-196\right)}}{2\times 4}$$

Multiply -16 times -196.

$$x=\frac{0±\sqrt{3136}}{2\times 4}$$

Take the square root of 3136.

$$x=\frac{0±56}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±56}{8}$$

Now solve the equation x=\frac{0±56}{8} when ± is plus. Divide 56 by 8.

$$x=7$$

Now solve the equation x=\frac{0±56}{8} when ± is minus. Divide -56 by 8.

$$x=-7$$

The equation is now solved.

$$x=7 x=-7$$