Solve 8x*9x=46

$$8x \times 9x=46$$

Solve for x

$$x=\frac{\sqrt{23}}{6}\approx 0.799305254$$

$$x=-\frac{\sqrt{23}}{6}\approx -0.799305254$$

Steps by Finding Square Root

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

$$8x^{2}\times 9=46$$

Multiply 8 and 9 to get 72.

$$72x^{2}=46$$

Divide both sides by 72.

$$x^{2}=\frac{46}{72}$$

Reduce the fraction \frac{46}{72} to lowest terms by extracting and canceling out 2.

$$x^{2}=\frac{23}{36}$$

Take the square root of both sides of the equation.

$$x=\frac{\sqrt{23}}{6} x=-\frac{\sqrt{23}}{6}$$

Steps Using the Quadratic Formula

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

$$8x^{2}\times 9=46$$

Multiply 8 and 9 to get 72.

$$72x^{2}=46$$

Subtract 46 from both sides.

$$72x^{2}-46=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 72 for a, 0 for b, and -46 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 72\left(-46\right)}}{2\times 72}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 72\left(-46\right)}}{2\times 72}$$

Multiply -4 times 72.

$$x=\frac{0±\sqrt{-288\left(-46\right)}}{2\times 72}$$

Multiply -288 times -46.

$$x=\frac{0±\sqrt{13248}}{2\times 72}$$

Take the square root of 13248.

$$x=\frac{0±24\sqrt{23}}{2\times 72}$$

Multiply 2 times 72.

$$x=\frac{0±24\sqrt{23}}{144}$$

Now solve the equation x=\frac{0±24\sqrt{23}}{144} when ± is plus.

$$x=\frac{\sqrt{23}}{6}$$

Now solve the equation x=\frac{0±24\sqrt{23}}{144} when ± is minus.

$$x=-\frac{\sqrt{23}}{6}$$

The equation is now solved.

$$x=\frac{\sqrt{23}}{6} x=-\frac{\sqrt{23}}{6}$$