Solve w*(w*1.25)=180

$$w \times ( w \times 1.25 ) = 180$$

Solve for w

$$w=12$$

$$w=-12$$

Steps by Finding Square Root

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

$$w^{2}\times 1.25=180$$

Divide both sides by 1.25.

$$w^{2}=\frac{180}{1.25}$$

Expand \frac{180}{1.25} by multiplying both numerator and the denominator by 100.

$$w^{2}=\frac{18000}{125}$$

Divide 18000 by 125 to get 144.

$$w^{2}=144$$

Take the square root of both sides of the equation.

$$w=12 w=-12$$

Steps Using the Quadratic Formula

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

$$w^{2}\times 1.25=180$$

Subtract 180 from both sides.

$$w^{2}\times 1.25-180=0$$

Quadratic equations like this one, with an x^{2} term but no x term, can still be solved using the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}, once they are put in standard form: ax^{2}+bx+c=0.

$$1.25w^{2}-180=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1.25 for a, 0 for b, and -180 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{0±\sqrt{0^{2}-4\times 1.25\left(-180\right)}}{2\times 1.25}$$

Square 0.

$$w=\frac{0±\sqrt{-4\times 1.25\left(-180\right)}}{2\times 1.25}$$

Multiply -4 times 1.25.

$$w=\frac{0±\sqrt{-5\left(-180\right)}}{2\times 1.25}$$

Multiply -5 times -180.

$$w=\frac{0±\sqrt{900}}{2\times 1.25}$$

Take the square root of 900.

$$w=\frac{0±30}{2\times 1.25}$$

Multiply 2 times 1.25.

$$w=\frac{0±30}{2.5}$$

Now solve the equation w=\frac{0±30}{2.5} when ± is plus. Divide 30 by 2.5 by multiplying 30 by the reciprocal of 2.5.

$$w=12$$

Now solve the equation w=\frac{0±30}{2.5} when ± is minus. Divide -30 by 2.5 by multiplying -30 by the reciprocal of 2.5.

$$w=-12$$

The equation is now solved.

$$w=12 w=-12$$