Solve 5w*w=405

$$5 w \times w = 405$$

Solve for w

$$w=9$$

$$w=-9$$

Steps by Finding Square Root

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

$$5w^{2}=405$$

Divide both sides by 5.

$$w^{2}=\frac{405}{5}$$

Divide 405 by 5 to get 81.

$$w^{2}=81$$

Take the square root of both sides of the equation.

$$w=9 w=-9$$

Steps Using the Quadratic Formula

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

$$5w^{2}=405$$

Subtract 405 from both sides.

$$5w^{2}-405=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, 0 for b, and -405 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$w=\frac{0±\sqrt{0^{2}-4\times 5\left(-405\right)}}{2\times 5}$$

Square 0.

$$w=\frac{0±\sqrt{-4\times 5\left(-405\right)}}{2\times 5}$$

Multiply -4 times 5.

$$w=\frac{0±\sqrt{-20\left(-405\right)}}{2\times 5}$$

Multiply -20 times -405.

$$w=\frac{0±\sqrt{8100}}{2\times 5}$$

Take the square root of 8100.

$$w=\frac{0±90}{2\times 5}$$

Multiply 2 times 5.

$$w=\frac{0±90}{10}$$

Now solve the equation w=\frac{0±90}{10} when ± is plus. Divide 90 by 10.

$$w=9$$

Now solve the equation w=\frac{0±90}{10} when ± is minus. Divide -90 by 10.

$$w=-9$$

The equation is now solved.

$$w=9 w=-9$$