Solve (-3/7)(7/p)=-1

$$( \frac { - 3 } { 7 } ) ( \frac { 7 } { p } ) = - 1$$

Solve for p

$$p=3$$

Steps Using Factoring

Variable p cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 7p, the least common multiple of 7,p.

$$p\left(-3\right)\times \frac{7}{p}=-7p$$

Express p\times \frac{7}{p} as a single fraction.

$$\frac{p\times 7}{p}\left(-3\right)=-7p$$

Express \frac{p\times 7}{p}\left(-3\right) as a single fraction.

$$\frac{-p\times 7\times 3}{p}=-7p$$

Add 7p to both sides.

$$\frac{-p\times 7\times 3}{p}+7p=0$$

Multiply -1 and 7 to get -7.

$$\frac{-7p\times 3}{p}+7p=0$$

Multiply -7 and 3 to get -21.

$$\frac{-21p}{p}+7p=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 7p times \frac{p}{p}.

$$\frac{-21p}{p}+\frac{7pp}{p}=0$$

Since \frac{-21p}{p} and \frac{7pp}{p} have the same denominator, add them by adding their numerators.

$$\frac{-21p+7pp}{p}=0$$

Do the multiplications in -21p+7pp.

$$\frac{-21p+7p^{2}}{p}=0$$

Variable p cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by p.

$$-21p+7p^{2}=0$$

Factor out p.

$$p\left(-21+7p\right)=0$$

To find equation solutions, solve p=0 and -21+7p=0.

$$p=0 p=3$$

Variable p cannot be equal to 0.

$$p=3$$

Steps Using the Quadratic Formula

Variable p cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 7p, the least common multiple of 7,p.

$$p\left(-3\right)\times \frac{7}{p}=-7p$$

Express p\times \frac{7}{p} as a single fraction.

$$\frac{p\times 7}{p}\left(-3\right)=-7p$$

Express \frac{p\times 7}{p}\left(-3\right) as a single fraction.

$$\frac{-p\times 7\times 3}{p}=-7p$$

Add 7p to both sides.

$$\frac{-p\times 7\times 3}{p}+7p=0$$

Multiply -1 and 7 to get -7.

$$\frac{-7p\times 3}{p}+7p=0$$

Multiply -7 and 3 to get -21.

$$\frac{-21p}{p}+7p=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 7p times \frac{p}{p}.

$$\frac{-21p}{p}+\frac{7pp}{p}=0$$

Since \frac{-21p}{p} and \frac{7pp}{p} have the same denominator, add them by adding their numerators.

$$\frac{-21p+7pp}{p}=0$$

Do the multiplications in -21p+7pp.

$$\frac{-21p+7p^{2}}{p}=0$$

Variable p cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by p.

$$-21p+7p^{2}=0$$

All equations of the form ax^{2}+bx+c=0 can be solved using the quadratic formula: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$$7p^{2}-21p=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 7 for a, -21 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$p=\frac{-\left(-21\right)±\sqrt{\left(-21\right)^{2}}}{2\times 7}$$

Take the square root of \left(-21\right)^{2}.

$$p=\frac{-\left(-21\right)±21}{2\times 7}$$

The opposite of -21 is 21.

$$p=\frac{21±21}{2\times 7}$$

Multiply 2 times 7.

$$p=\frac{21±21}{14}$$

Now solve the equation p=\frac{21±21}{14} when ± is plus. Add 21 to 21.

$$p=\frac{42}{14}$$

Divide 42 by 14.

$$p=3$$

Now solve the equation p=\frac{21±21}{14} when ± is minus. Subtract 21 from 21.

$$p=\frac{0}{14}$$

Divide 0 by 14.

$$p=0$$

The equation is now solved.

$$p=3 p=0$$

Variable p cannot be equal to 0.

$$p=3$$

Steps for Completing the Square

Variable p cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 7p, the least common multiple of 7,p.

$$p\left(-3\right)\times \frac{7}{p}=-7p$$

Express p\times \frac{7}{p} as a single fraction.

$$\frac{p\times 7}{p}\left(-3\right)=-7p$$

Express \frac{p\times 7}{p}\left(-3\right) as a single fraction.

$$\frac{-p\times 7\times 3}{p}=-7p$$

Add 7p to both sides.

$$\frac{-p\times 7\times 3}{p}+7p=0$$

Multiply -1 and 7 to get -7.

$$\frac{-7p\times 3}{p}+7p=0$$

Multiply -7 and 3 to get -21.

$$\frac{-21p}{p}+7p=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 7p times \frac{p}{p}.

$$\frac{-21p}{p}+\frac{7pp}{p}=0$$

Since \frac{-21p}{p} and \frac{7pp}{p} have the same denominator, add them by adding their numerators.

$$\frac{-21p+7pp}{p}=0$$

Do the multiplications in -21p+7pp.

$$\frac{-21p+7p^{2}}{p}=0$$

Variable p cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by p.

$$-21p+7p^{2}=0$$

Quadratic equations such as this one can be solved by completing the square. In order to complete the square, the equation must first be in the form x^{2}+bx=c.

$$7p^{2}-21p=0$$

Divide both sides by 7.

$$\frac{7p^{2}-21p}{7}=\frac{0}{7}$$

Dividing by 7 undoes the multiplication by 7.

$$p^{2}+\left(-\frac{21}{7}\right)p=\frac{0}{7}$$

Divide -21 by 7.

$$p^{2}-3p=\frac{0}{7}$$

Divide 0 by 7.

$$p^{2}-3p=0$$

Divide -3, the coefficient of the x term, by 2 to get -\frac{3}{2}. Then add the square of -\frac{3}{2} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$p^{2}-3p+\left(-\frac{3}{2}\right)^{2}=\left(-\frac{3}{2}\right)^{2}$$

Square -\frac{3}{2} by squaring both the numerator and the denominator of the fraction.

$$p^{2}-3p+\frac{9}{4}=\frac{9}{4}$$

Factor p^{2}-3p+\frac{9}{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}.

$$\left(p-\frac{3}{2}\right)^{2}=\frac{9}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(p-\frac{3}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Simplify.

$$p-\frac{3}{2}=\frac{3}{2} p-\frac{3}{2}=-\frac{3}{2}$$

Add \frac{3}{2} to both sides of the equation.

$$p=3 p=0$$

Variable p cannot be equal to 0.

$$p=3$$