Solve x^2=1125*7/15*22

$$x ^ { 2 } = \frac { 1125 \times 7 } { 15 \times 22 }$$

Solve for x

$$x = \frac{5 \sqrt{462}}{22} \approx 4.885042105$$

$$x = -\frac{5 \sqrt{462}}{22} \approx -4.885042105$$

Steps by Finding Square Root

Cancel out 15 in both numerator and denominator.

$$x^{2}=\frac{7\times 75}{22}$$

Multiply 7 and 75 to get 525.

$$x^{2}=\frac{525}{22}$$

Take the square root of both sides of the equation.

$$x=\frac{5\sqrt{462}}{22} x=-\frac{5\sqrt{462}}{22}$$

Steps Using the Quadratic Formula

Cancel out 15 in both numerator and denominator.

$$x^{2}=\frac{7\times 75}{22}$$

Multiply 7 and 75 to get 525.

$$x^{2}=\frac{525}{22}$$

Subtract \frac{525}{22} from both sides.

$$x^{2}-\frac{525}{22}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -\frac{525}{22} for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-\frac{525}{22}\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-\frac{525}{22}\right)}}{2}$$

Multiply -4 times -\frac{525}{22}.

$$x=\frac{0±\sqrt{\frac{1050}{11}}}{2}$$

Take the square root of \frac{1050}{11}.

$$x=\frac{0±\frac{5\sqrt{462}}{11}}{2}$$

Now solve the equation x=\frac{0±\frac{5\sqrt{462}}{11}}{2} when ± is plus.

$$x=\frac{5\sqrt{462}}{22}$$

Now solve the equation x=\frac{0±\frac{5\sqrt{462}}{11}}{2} when ± is minus.

$$x=-\frac{5\sqrt{462}}{22}$$

The equation is now solved.

$$x=\frac{5\sqrt{462}}{22} x=-\frac{5\sqrt{462}}{22}$$