Solve 4x^2-36=74

$$4 { x }^{ 2 } -36 = 74$$

Solve for x

$$x = \frac{\sqrt{110}}{2} \approx 5.244044241$$

$$x = -\frac{\sqrt{110}}{2} \approx -5.244044241$$

Steps by Finding Square Root

Add 36 to both sides.

$$4x^{2}=74+36$$

Add 74 and 36 to get 110.

$$4x^{2}=110$$

Divide both sides by 4.

$$x^{2}=\frac{110}{4}$$

Reduce the fraction \frac{110}{4} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{55}{2}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{110}}{2} x=-\frac{\sqrt{110}}{2}$$

Steps Using the Quadratic Formula

Subtract 74 from both sides.

$$4x^{2}-36-74=0$$

Subtract 74 from -36 to get -110.

$$4x^{2}-110=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -110 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-110\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-110\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-110\right)}}{2\times 4}$$

Multiply -16 times -110.

$$x=\frac{0±\sqrt{1760}}{2\times 4}$$

Take the square root of 1760.

$$x=\frac{0±4\sqrt{110}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±4\sqrt{110}}{8}$$

Now solve the equation x=\frac{0±4\sqrt{110}}{8} when ± is plus.

$$x=\frac{\sqrt{110}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{110}}{8} when ± is minus.

$$x=-\frac{\sqrt{110}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{110}}{2} x=-\frac{\sqrt{110}}{2}$$