Solve 5p^2=35p

$$5 p ^ { 2 } = 35 p$$

Solve for p

$$p=7$$

$$p=0$$

Steps Using Factoring

Subtract 35p from both sides.

$$5p^{2}-35p=0$$

Factor out p.

$$p\left(5p-35\right)=0$$

To find equation solutions, solve p=0 and 5p-35=0.

$$p=0 p=7$$

Steps Using the Quadratic Formula

Subtract 35p from both sides.

$$5p^{2}-35p=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 5 for a, -35 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{-\left(-35\right)±\sqrt{\left(-35\right)^{2}}}{2\times 5}$$

Take the square root of \left(-35\right)^{2}.

$$p=\frac{-\left(-35\right)±35}{2\times 5}$$

The opposite of -35 is 35.

$$p=\frac{35±35}{2\times 5}$$

Multiply 2 times 5.

$$p=\frac{35±35}{10}$$

Now solve the equation p=\frac{35±35}{10} when ± is plus. Add 35 to 35.

$$p=\frac{70}{10}$$

Divide 70 by 10.

$$p=7$$

Now solve the equation p=\frac{35±35}{10} when ± is minus. Subtract 35 from 35.

$$p=\frac{0}{10}$$

Divide 0 by 10.

$$p=0$$

The equation is now solved.

$$p=7 p=0$$

Steps for Completing the Square

Subtract 35p from both sides.

$$5p^{2}-35p=0$$

Divide both sides by 5.

$$\frac{5p^{2}-35p}{5}=\frac{0}{5}$$

Dividing by 5 undoes the multiplication by 5.

$$p^{2}+\left(-\frac{35}{5}\right)p=\frac{0}{5}$$

Divide -35 by 5.

$$p^{2}-7p=\frac{0}{5}$$

Divide 0 by 5.

$$p^{2}-7p=0$$

Divide -7, the coefficient of the x term, by 2 to get -\frac{7}{2}. Then add the square of -\frac{7}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$p^{2}-7p+\left(-\frac{7}{2}\right)^{2}=\left(-\frac{7}{2}\right)^{2}$$

Square -\frac{7}{2} by squaring both the numerator and the denominator of the fraction.

$$p^{2}-7p+\frac{49}{4}=\frac{49}{4}$$

Factor p^{2}-7p+\frac{49}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(p-\frac{7}{2}\right)^{2}=\frac{49}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(p-\frac{7}{2}\right)^{2}}=\sqrt{\frac{49}{4}}$$

Simplify.

$$p-\frac{7}{2}=\frac{7}{2} p-\frac{7}{2}=-\frac{7}{2}$$

Add \frac{7}{2} to both sides of the equation.

$$p=7 p=0$$