Basic Math Examples

${(3 t + 5)}^{2} = 7$

Step 1

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

$3 t + 5 = \pm \sqrt{7}$

Step 2

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

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Step 2.1

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

$3 t + 5 = \sqrt{7}$

Step 2.2

Subtract $5$ from both sides of the equation.

$3 t = \sqrt{7} - 5$

Step 2.3

Divide each term in $3 t = \sqrt{7} - 5$ by $3$ and simplify.

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Step 2.3.1

Divide each term in $3 t = \sqrt{7} - 5$ by $3$ .

$\frac{3 t}{3} = \frac{\sqrt{7}}{3} + \frac{- 5}{3}$

Step 2.3.2

Simplify the left side.

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Step 2.3.2.1

Cancel the common factor of $3$ .

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Step 2.3.2.1.1

Cancel the common factor.

$\frac{3 t}{3} = \frac{\sqrt{7}}{3} + \frac{- 5}{3}$

Step 2.3.2.1.2

Divide $t$ by $1$ .

$t = \frac{\sqrt{7}}{3} + \frac{- 5}{3}$

Step 2.3.3

Simplify the right side.

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Step 2.3.3.1

Move the negative in front of the fraction.

$t = \frac{\sqrt{7}}{3} - \frac{5}{3}$

Step 2.4

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

$3 t + 5 = - \sqrt{7}$

Step 2.5

Subtract $5$ from both sides of the equation.

$3 t = - \sqrt{7} - 5$

Step 2.6

Divide each term in $3 t = - \sqrt{7} - 5$ by $3$ and simplify.

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Step 2.6.1

Divide each term in $3 t = - \sqrt{7} - 5$ by $3$ .

$\frac{3 t}{3} = \frac{- \sqrt{7}}{3} + \frac{- 5}{3}$

Step 2.6.2

Simplify the left side.

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Step 2.6.2.1

Cancel the common factor of $3$ .

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Step 2.6.2.1.1

Cancel the common factor.

$\frac{3 t}{3} = \frac{- \sqrt{7}}{3} + \frac{- 5}{3}$

Step 2.6.2.1.2

Divide $t$ by $1$ .

$t = \frac{- \sqrt{7}}{3} + \frac{- 5}{3}$

Step 2.6.3

Simplify the right side.

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Step 2.6.3.1

Simplify each term.

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Step 2.6.3.1.1

Move the negative in front of the fraction.

$t = - \frac{\sqrt{7}}{3} + \frac{- 5}{3}$

Step 2.6.3.1.2

Move the negative in front of the fraction.

$t = - \frac{\sqrt{7}}{3} - \frac{5}{3}$

Step 2.7

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

$t = \frac{\sqrt{7}}{3} - \frac{5}{3}, - \frac{\sqrt{7}}{3} - \frac{5}{3}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$t = \frac{\sqrt{7}}{3} - \frac{5}{3}, - \frac{\sqrt{7}}{3} - \frac{5}{3}$

Decimal Form:

$t = - 0.78474956 \dots, - 2.54858377 \dots$