Solve 4x^2+5=100

$$4 x ^ { 2 } + 5 = 100$$

Solve for x

$$x = \frac{\sqrt{95}}{2} \approx 4.873397172$$

$$x = -\frac{\sqrt{95}}{2} \approx -4.873397172$$

Steps by Finding Square Root

Subtract 5 from both sides.

$$4x^{2}=100-5$$

Subtract 5 from 100 to get 95.

$$4x^{2}=95$$

Divide both sides by 4.

$$x^{2}=\frac{95}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{95}}{2} x=-\frac{\sqrt{95}}{2}$$

Steps Using the Quadratic Formula

Subtract 100 from both sides.

$$4x^{2}+5-100=0$$

Subtract 100 from 5 to get -95.

$$4x^{2}-95=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -95 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-95\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-95\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-95\right)}}{2\times 4}$$

Multiply -16 times -95.

$$x=\frac{0±\sqrt{1520}}{2\times 4}$$

Take the square root of 1520.

$$x=\frac{0±4\sqrt{95}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±4\sqrt{95}}{8}$$

Now solve the equation x=\frac{0±4\sqrt{95}}{8} when ± is plus.

$$x=\frac{\sqrt{95}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{95}}{8} when ± is minus.

$$x=-\frac{\sqrt{95}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{95}}{2} x=-\frac{\sqrt{95}}{2}$$