Solve (4x)x=165

$$(4x)x=165$$

Solve for x

$$x = \frac{\sqrt{165}}{2} \approx 6.422616289$$

$$x = -\frac{\sqrt{165}}{2} \approx -6.422616289$$

Steps by Finding Square Root

Multiply x and x to get x^{2}.

$$4x^{2}=165$$

Divide both sides by 4.

$$x^{2}=\frac{165}{4}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{165}}{2} x=-\frac{\sqrt{165}}{2}$$

Steps Using the Quadratic Formula

Multiply x and x to get x^{2}.

$$4x^{2}=165$$

Subtract 165 from both sides.

$$4x^{2}-165=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 4 for a, 0 for b, and -165 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 4\left(-165\right)}}{2\times 4}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 4\left(-165\right)}}{2\times 4}$$

Multiply -4 times 4.

$$x=\frac{0±\sqrt{-16\left(-165\right)}}{2\times 4}$$

Multiply -16 times -165.

$$x=\frac{0±\sqrt{2640}}{2\times 4}$$

Take the square root of 2640.

$$x=\frac{0±4\sqrt{165}}{2\times 4}$$

Multiply 2 times 4.

$$x=\frac{0±4\sqrt{165}}{8}$$

Now solve the equation x=\frac{0±4\sqrt{165}}{8} when ± is plus.

$$x=\frac{\sqrt{165}}{2}$$

Now solve the equation x=\frac{0±4\sqrt{165}}{8} when ± is minus.

$$x=-\frac{\sqrt{165}}{2}$$

The equation is now solved.

$$x=\frac{\sqrt{165}}{2} x=-\frac{\sqrt{165}}{2}$$