Solve 26%1/R_{p}=1/12+1/12+1/12=

$$26 \% \frac { 1 } { R _ { p } } = \frac { 1 } { 12 } + \frac { 1 } { 12 } + \frac { 1 } { 12 } =$$

Solve for R_p

$$R_{p} = \frac{26}{25} = 1\frac{1}{25} = 1.04$$

Steps Using Factoring

Variable R_{p} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 300R_{p}, the least common multiple of 100,R_{p},12.

$$3R_{p}\times 26\times \frac{1}{R_{p}}=300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}$$

Multiply 3 and 26 to get 78.

$$78R_{p}\times \frac{1}{R_{p}}=300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}$$

Express 78\times \frac{1}{R_{p}} as a single fraction.

$$\frac{78}{R_{p}}R_{p}=300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}$$

Multiply 300 and \frac{1}{12} to get \frac{300}{12}.

$$\frac{78}{R_{p}}R_{p}=\frac{300}{12}R_{p}+300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}$$

Divide 300 by 12 to get 25.

$$\frac{78}{R_{p}}R_{p}=25R_{p}+300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}$$

Multiply 300 and \frac{1}{12} to get \frac{300}{12}.

$$\frac{78}{R_{p}}R_{p}=25R_{p}+\frac{300}{12}R_{p}+300R_{p}\times \frac{1}{12}$$

Divide 300 by 12 to get 25.

$$\frac{78}{R_{p}}R_{p}=25R_{p}+25R_{p}+300R_{p}\times \frac{1}{12}$$

Combine 25R_{p} and 25R_{p} to get 50R_{p}.

$$\frac{78}{R_{p}}R_{p}=50R_{p}+300R_{p}\times \frac{1}{12}$$

Multiply 300 and \frac{1}{12} to get \frac{300}{12}.

$$\frac{78}{R_{p}}R_{p}=50R_{p}+\frac{300}{12}R_{p}$$

Divide 300 by 12 to get 25.

$$\frac{78}{R_{p}}R_{p}=50R_{p}+25R_{p}$$

Combine 50R_{p} and 25R_{p} to get 75R_{p}.

$$\frac{78}{R_{p}}R_{p}=75R_{p}$$

Express \frac{78}{R_{p}}R_{p} as a single fraction.

$$\frac{78R_{p}}{R_{p}}=75R_{p}$$

Subtract 75R_{p} from both sides.

$$\frac{78R_{p}}{R_{p}}-75R_{p}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -75R_{p} times \frac{R_{p}}{R_{p}}.

$$\frac{78R_{p}}{R_{p}}+\frac{-75R_{p}R_{p}}{R_{p}}=0$$

Since \frac{78R_{p}}{R_{p}} and \frac{-75R_{p}R_{p}}{R_{p}} have the same denominator, add them by adding their numerators.

$$\frac{78R_{p}-75R_{p}R_{p}}{R_{p}}=0$$

Do the multiplications in 78R_{p}-75R_{p}R_{p}.

$$\frac{78R_{p}-75R_{p}^{2}}{R_{p}}=0$$

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

$$78R_{p}-75R_{p}^{2}=0$$

Factor out R_{p}.

$$R_{p}\left(78-75R_{p}\right)=0$$

To find equation solutions, solve R_{p}=0 and 78-75R_{p}=0.

$$R_{p}=0 R_{p}=\frac{26}{25}$$

Variable R_{p} cannot be equal to 0.

$$R_{p}=\frac{26}{25}$$

Steps Using the Quadratic Formula

Variable R_{p} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 300R_{p}, the least common multiple of 100,R_{p},12.

$$3R_{p}\times 26\times \frac{1}{R_{p}}=300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}$$

Multiply 3 and 26 to get 78.

$$78R_{p}\times \frac{1}{R_{p}}=300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}$$

Express 78\times \frac{1}{R_{p}} as a single fraction.

$$\frac{78}{R_{p}}R_{p}=300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}$$

Multiply 300 and \frac{1}{12} to get \frac{300}{12}.

$$\frac{78}{R_{p}}R_{p}=\frac{300}{12}R_{p}+300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}$$

Divide 300 by 12 to get 25.

$$\frac{78}{R_{p}}R_{p}=25R_{p}+300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}$$

Multiply 300 and \frac{1}{12} to get \frac{300}{12}.

$$\frac{78}{R_{p}}R_{p}=25R_{p}+\frac{300}{12}R_{p}+300R_{p}\times \frac{1}{12}$$

Divide 300 by 12 to get 25.

$$\frac{78}{R_{p}}R_{p}=25R_{p}+25R_{p}+300R_{p}\times \frac{1}{12}$$

Combine 25R_{p} and 25R_{p} to get 50R_{p}.

$$\frac{78}{R_{p}}R_{p}=50R_{p}+300R_{p}\times \frac{1}{12}$$

Multiply 300 and \frac{1}{12} to get \frac{300}{12}.

$$\frac{78}{R_{p}}R_{p}=50R_{p}+\frac{300}{12}R_{p}$$

Divide 300 by 12 to get 25.

$$\frac{78}{R_{p}}R_{p}=50R_{p}+25R_{p}$$

Combine 50R_{p} and 25R_{p} to get 75R_{p}.

$$\frac{78}{R_{p}}R_{p}=75R_{p}$$

Express \frac{78}{R_{p}}R_{p} as a single fraction.

$$\frac{78R_{p}}{R_{p}}=75R_{p}$$

Subtract 75R_{p} from both sides.

$$\frac{78R_{p}}{R_{p}}-75R_{p}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -75R_{p} times \frac{R_{p}}{R_{p}}.

$$\frac{78R_{p}}{R_{p}}+\frac{-75R_{p}R_{p}}{R_{p}}=0$$

Since \frac{78R_{p}}{R_{p}} and \frac{-75R_{p}R_{p}}{R_{p}} have the same denominator, add them by adding their numerators.

$$\frac{78R_{p}-75R_{p}R_{p}}{R_{p}}=0$$

Do the multiplications in 78R_{p}-75R_{p}R_{p}.

$$\frac{78R_{p}-75R_{p}^{2}}{R_{p}}=0$$

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

$$78R_{p}-75R_{p}^{2}=0$$

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.

$$-75R_{p}^{2}+78R_{p}=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute -75 for a, 78 for b, and 0 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$R_{p}=\frac{-78±\sqrt{78^{2}}}{2\left(-75\right)}$$

Take the square root of 78^{2}.

$$R_{p}=\frac{-78±78}{2\left(-75\right)}$$

Multiply 2 times -75.

$$R_{p}=\frac{-78±78}{-150}$$

Now solve the equation R_{p}=\frac{-78±78}{-150} when ± is plus. Add -78 to 78.

$$R_{p}=\frac{0}{-150}$$

Divide 0 by -150.

$$R_{p}=0$$

Now solve the equation R_{p}=\frac{-78±78}{-150} when ± is minus. Subtract 78 from -78.

$$R_{p}=-\frac{156}{-150}$$

Reduce the fraction \frac{-156}{-150} to lowest terms by extracting and canceling out 6.

$$R_{p}=\frac{26}{25}$$

The equation is now solved.

$$R_{p}=0 R_{p}=\frac{26}{25}$$

Variable R_{p} cannot be equal to 0.

$$R_{p}=\frac{26}{25}$$

Steps for Completing the Square

Variable R_{p} cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 300R_{p}, the least common multiple of 100,R_{p},12.

$$3R_{p}\times 26\times \frac{1}{R_{p}}=300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}$$

Multiply 3 and 26 to get 78.

$$78R_{p}\times \frac{1}{R_{p}}=300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}$$

Express 78\times \frac{1}{R_{p}} as a single fraction.

$$\frac{78}{R_{p}}R_{p}=300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}$$

Multiply 300 and \frac{1}{12} to get \frac{300}{12}.

$$\frac{78}{R_{p}}R_{p}=\frac{300}{12}R_{p}+300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}$$

Divide 300 by 12 to get 25.

$$\frac{78}{R_{p}}R_{p}=25R_{p}+300R_{p}\times \frac{1}{12}+300R_{p}\times \frac{1}{12}$$

Multiply 300 and \frac{1}{12} to get \frac{300}{12}.

$$\frac{78}{R_{p}}R_{p}=25R_{p}+\frac{300}{12}R_{p}+300R_{p}\times \frac{1}{12}$$

Divide 300 by 12 to get 25.

$$\frac{78}{R_{p}}R_{p}=25R_{p}+25R_{p}+300R_{p}\times \frac{1}{12}$$

Combine 25R_{p} and 25R_{p} to get 50R_{p}.

$$\frac{78}{R_{p}}R_{p}=50R_{p}+300R_{p}\times \frac{1}{12}$$

Multiply 300 and \frac{1}{12} to get \frac{300}{12}.

$$\frac{78}{R_{p}}R_{p}=50R_{p}+\frac{300}{12}R_{p}$$

Divide 300 by 12 to get 25.

$$\frac{78}{R_{p}}R_{p}=50R_{p}+25R_{p}$$

Combine 50R_{p} and 25R_{p} to get 75R_{p}.

$$\frac{78}{R_{p}}R_{p}=75R_{p}$$

Express \frac{78}{R_{p}}R_{p} as a single fraction.

$$\frac{78R_{p}}{R_{p}}=75R_{p}$$

Subtract 75R_{p} from both sides.

$$\frac{78R_{p}}{R_{p}}-75R_{p}=0$$

To add or subtract expressions, expand them to make their denominators the same. Multiply -75R_{p} times \frac{R_{p}}{R_{p}}.

$$\frac{78R_{p}}{R_{p}}+\frac{-75R_{p}R_{p}}{R_{p}}=0$$

Since \frac{78R_{p}}{R_{p}} and \frac{-75R_{p}R_{p}}{R_{p}} have the same denominator, add them by adding their numerators.

$$\frac{78R_{p}-75R_{p}R_{p}}{R_{p}}=0$$

Do the multiplications in 78R_{p}-75R_{p}R_{p}.

$$\frac{78R_{p}-75R_{p}^{2}}{R_{p}}=0$$

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

$$78R_{p}-75R_{p}^{2}=0$$

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.

$$-75R_{p}^{2}+78R_{p}=0$$

Divide both sides by -75.

$$\frac{-75R_{p}^{2}+78R_{p}}{-75}=\frac{0}{-75}$$

Dividing by -75 undoes the multiplication by -75.

$$R_{p}^{2}+\frac{78}{-75}R_{p}=\frac{0}{-75}$$

Reduce the fraction \frac{78}{-75} to lowest terms by extracting and canceling out 3.

$$R_{p}^{2}-\frac{26}{25}R_{p}=\frac{0}{-75}$$

Divide 0 by -75.

$$R_{p}^{2}-\frac{26}{25}R_{p}=0$$

Divide -\frac{26}{25}, the coefficient of the x term, by 2 to get -\frac{13}{25}. Then add the square of -\frac{13}{25} to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$R_{p}^{2}-\frac{26}{25}R_{p}+\left(-\frac{13}{25}\right)^{2}=\left(-\frac{13}{25}\right)^{2}$$

Square -\frac{13}{25} by squaring both the numerator and the denominator of the fraction.

$$R_{p}^{2}-\frac{26}{25}R_{p}+\frac{169}{625}=\frac{169}{625}$$

Factor R_{p}^{2}-\frac{26}{25}R_{p}+\frac{169}{625}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(R_{p}-\frac{13}{25}\right)^{2}=\frac{169}{625}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(R_{p}-\frac{13}{25}\right)^{2}}=\sqrt{\frac{169}{625}}$$

Simplify.

$$R_{p}-\frac{13}{25}=\frac{13}{25} R_{p}-\frac{13}{25}=-\frac{13}{25}$$

Add \frac{13}{25} to both sides of the equation.

$$R_{p}=\frac{26}{25} R_{p}=0$$

Variable R_{p} cannot be equal to 0.

$$R_{p}=\frac{26}{25}$$