Solve 4x^2-30=34

$$4 x ^ { 2 } - 30 = 34$$

Solve for x

$$x=4$$

$$x=-4$$

Steps Using Difference of Squares

Subtract 34 from both sides.

$$4x^{2}-30-34=0$$

Subtract 34 from -30 to get -64.

$$4x^{2}-64=0$$

Divide both sides by 4.

$$x^{2}-16=0$$

Consider x^{2}-16. Rewrite x^{2}-16 as x^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-4\right)\left(x+4\right)=0$$

To find equation solutions, solve x-4=0 and x+4=0.

$$x=4 x=-4$$

Steps by Finding Square Root

Add 30 to both sides.

$$4x^{2}=34+30$$

Add 34 and 30 to get 64.

$$4x^{2}=64$$

Divide both sides by 4.

$$x^{2}=\frac{64}{4}$$

Divide 64 by 4 to get 16.

$$x^{2}=16$$

Take the square root of both sides of the equation.

$$x=4 x=-4$$

Steps Using the Quadratic Formula

Subtract 34 from both sides.

$$4x^{2}-30-34=0$$

Subtract 34 from -30 to get -64.

$$4x^{2}-64=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -64 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-64\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-64\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-64\right)}}{2\times 4}$$

Multiply -16 times -64.

$$x=\frac{0±\sqrt{1024}}{2\times 4}$$

Take the square root of 1024.

$$x=\frac{0±32}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±32}{8}$$

Now solve the equation x=\frac{0±32}{8} when ± is plus. Divide 32 by 8.

$$x=4$$

Now solve the equation x=\frac{0±32}{8} when ± is minus. Divide -32 by 8.

$$x=-4$$

The equation is now solved.

$$x=4 x=-4$$