Solve 4x^2+4=100

$$4 x ^ { 2 } + 4 = 100$$

Solve for x

$$x=2\sqrt{6}\approx 4.898979486$$

$$x=-2\sqrt{6}\approx -4.898979486$$

Steps by Finding Square Root

Subtract 4 from both sides.

$$4x^{2}=100-4$$

Subtract 4 from 100 to get 96.

$$4x^{2}=96$$

Divide both sides by 4.

$$x^{2}=\frac{96}{4}$$

Divide 96 by 4 to get 24.

$$x^{2}=24$$

Take the square root of both sides of the equation.

$$x=2\sqrt{6} x=-2\sqrt{6}$$

Steps Using the Quadratic Formula

Subtract 100 from both sides.

$$4x^{2}+4-100=0$$

Subtract 100 from 4 to get -96.

$$4x^{2}-96=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -96 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-96\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-96\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-96\right)}}{2\times 4}$$

Multiply -16 times -96.

$$x=\frac{0±\sqrt{1536}}{2\times 4}$$

Take the square root of 1536.

$$x=\frac{0±16\sqrt{6}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±16\sqrt{6}}{8}$$

Now solve the equation x=\frac{0±16\sqrt{6}}{8} when ± is plus.

$$x=2\sqrt{6}$$

Now solve the equation x=\frac{0±16\sqrt{6}}{8} when ± is minus.

$$x=-2\sqrt{6}$$

The equation is now solved.

$$x=2\sqrt{6} x=-2\sqrt{6}$$