Solve 4x*5x=10

$$4x \times 5x=10$$

Solve for x

$$x=\frac{\sqrt{2}}{2}\approx 0.707106781$$

$$x=-\frac{\sqrt{2}}{2}\approx -0.707106781$$

Steps by Finding Square Root

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

$$4x^{2}\times 5=10$$

Multiply 4 and 5 to get 20.

$$20x^{2}=10$$

Divide both sides by 20.

$$x^{2}=\frac{10}{20}$$

Reduce the fraction \frac{10}{20} to lowest terms by extracting and canceling out 10.

$$x^{2}=\frac{1}{2}$$

Take the square root of both sides of the equation.

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

Steps Using the Quadratic Formula

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

$$4x^{2}\times 5=10$$

Multiply 4 and 5 to get 20.

$$20x^{2}=10$$

Subtract 10 from both sides.

$$20x^{2}-10=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 20 for a, 0 for b, and -10 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 20\left(-10\right)}}{2\times 20}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 20\left(-10\right)}}{2\times 20}$$

Multiply -4 times 20.

$$x=\frac{0±\sqrt{-80\left(-10\right)}}{2\times 20}$$

Multiply -80 times -10.

$$x=\frac{0±\sqrt{800}}{2\times 20}$$

Take the square root of 800.

$$x=\frac{0±20\sqrt{2}}{2\times 20}$$

Multiply 2 times 20.

$$x=\frac{0±20\sqrt{2}}{40}$$

Now solve the equation x=\frac{0±20\sqrt{2}}{40} when ± is plus.

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

Now solve the equation x=\frac{0±20\sqrt{2}}{40} when ± is minus.

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

The equation is now solved.

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