Solve 224=90x*10x

$$224 = 90 x \cdot 10 x$$

Solve for x

$$x=\frac{2\sqrt{14}}{15}\approx 0.498887652$$

$$x=-\frac{2\sqrt{14}}{15}\approx -0.498887652$$

Steps by Finding Square Root

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

$$224=90x^{2}\times 10$$

Multiply 90 and 10 to get 900.

$$224=900x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$900x^{2}=224$$

Divide both sides by 900.

$$x^{2}=\frac{224}{900}$$

Reduce the fraction \frac{224}{900} to lowest terms by extracting and canceling out 4.

$$x^{2}=\frac{56}{225}$$

Take the square root of both sides of the equation.

$$x=\frac{2\sqrt{14}}{15} x=-\frac{2\sqrt{14}}{15}$$

Steps Using the Quadratic Formula

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

$$224=90x^{2}\times 10$$

Multiply 90 and 10 to get 900.

$$224=900x^{2}$$

Swap sides so that all variable terms are on the left hand side.

$$900x^{2}=224$$

Subtract 224 from both sides.

$$900x^{2}-224=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 900 for a, 0 for b, and -224 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 900\left(-224\right)}}{2\times 900}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 900\left(-224\right)}}{2\times 900}$$

Multiply -4 times 900.

$$x=\frac{0±\sqrt{-3600\left(-224\right)}}{2\times 900}$$

Multiply -3600 times -224.

$$x=\frac{0±\sqrt{806400}}{2\times 900}$$

Take the square root of 806400.

$$x=\frac{0±240\sqrt{14}}{2\times 900}$$

Multiply 2 times 900.

$$x=\frac{0±240\sqrt{14}}{1800}$$

Now solve the equation x=\frac{0±240\sqrt{14}}{1800} when ± is plus.

$$x=\frac{2\sqrt{14}}{15}$$

Now solve the equation x=\frac{0±240\sqrt{14}}{1800} when ± is minus.

$$x=-\frac{2\sqrt{14}}{15}$$

The equation is now solved.

$$x=\frac{2\sqrt{14}}{15} x=-\frac{2\sqrt{14}}{15}$$