Algebra Examples

$\frac{5 p + q^{2}}{7} = 8$

Step 1

Multiply both sides by $7$ .

$\frac{5 p + q^{2}}{7} \cdot 7 = 8 \cdot 7$

Step 2

Simplify.

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Step 2.1

Simplify the left side.

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Step 2.1.1

Simplify $\frac{5 p + q^{2}}{7} \cdot 7$ .

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Step 2.1.1.1

Cancel the common factor of $7$ .

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Step 2.1.1.1.1

Cancel the common factor.

$\frac{5 p + q^{2}}{7} \cdot 7 = 8 \cdot 7$

Step 2.1.1.1.2

Rewrite the expression.

$5 p + q^{2} = 8 \cdot 7$

Step 2.1.1.2

Reorder $5 p$ and $q^{2}$ .

$q^{2} + 5 p = 8 \cdot 7$

Step 2.2

Simplify the right side.

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Step 2.2.1

Multiply $8$ by $7$ .

$q^{2} + 5 p = 56$

Step 3

Solve for $q$ .

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Step 3.1

Subtract $5 p$ from both sides of the equation.

$q^{2} = 56 - 5 p$

Step 3.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$q = \pm \sqrt{56 - 5 p}$

Step 3.3

The complete solution is the result of both the positive and negative portions of the solution.

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Step 3.3.1

First, use the positive value of the $\pm$ to find the first solution.

$q = \sqrt{56 - 5 p}$

Step 3.3.2

Next, use the negative value of the $\pm$ to find the second solution.

$q = - \sqrt{56 - 5 p}$

Step 3.3.3

The complete solution is the result of both the positive and negative portions of the solution.

$q = \sqrt{56 - 5 p}$

$q = - \sqrt{56 - 5 p}$

$q = \sqrt{56 - 5 p}$

$q = - \sqrt{56 - 5 p}$

$q = \sqrt{56 - 5 p}$

$q = - \sqrt{56 - 5 p}$