Algebra Examples

$3 {(5 x + 5)}^{2} - 47 = 10$

Step 1

Add $47$ to both sides of the equation.

$3 {(5 x + 5)}^{2} = 10 + 47$

Step 2

Add $10$ and $47$ .

$3 {(5 x + 5)}^{2} = 57$

Step 3

Divide each term in $3 {(5 x + 5)}^{2} = 57$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 {(5 x + 5)}^{2} = 57$ by $3$ .

$\frac{3 {(5 x + 5)}^{2}}{3} = \frac{57}{3}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $3$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{3 {(5 x + 5)}^{2}}{3} = \frac{57}{3}$

Step 3.2.1.2

Divide ${(5 x + 5)}^{2}$ by $1$ .

${(5 x + 5)}^{2} = \frac{57}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $57$ by $3$ .

${(5 x + 5)}^{2} = 19$

Step 4

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

$5 x + 5 = \pm \sqrt{19}$

Step 5

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

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Step 5.1

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

$5 x + 5 = \sqrt{19}$

Step 5.2

Subtract $5$ from both sides of the equation.

$5 x = \sqrt{19} - 5$

Step 5.3

Divide each term in $5 x = \sqrt{19} - 5$ by $5$ and simplify.

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Step 5.3.1

Divide each term in $5 x = \sqrt{19} - 5$ by $5$ .

$\frac{5 x}{5} = \frac{\sqrt{19}}{5} + \frac{- 5}{5}$

Step 5.3.2

Simplify the left side.

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Step 5.3.2.1

Cancel the common factor of $5$ .

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Step 5.3.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{\sqrt{19}}{5} + \frac{- 5}{5}$

Step 5.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\sqrt{19}}{5} + \frac{- 5}{5}$

Step 5.3.3

Simplify the right side.

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Step 5.3.3.1

Divide $- 5$ by $5$ .

$x = \frac{\sqrt{19}}{5} - 1$

Step 5.4

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

$5 x + 5 = - \sqrt{19}$

Step 5.5

Subtract $5$ from both sides of the equation.

$5 x = - \sqrt{19} - 5$

Step 5.6

Divide each term in $5 x = - \sqrt{19} - 5$ by $5$ and simplify.

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Step 5.6.1

Divide each term in $5 x = - \sqrt{19} - 5$ by $5$ .

$\frac{5 x}{5} = \frac{- \sqrt{19}}{5} + \frac{- 5}{5}$

Step 5.6.2

Simplify the left side.

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Step 5.6.2.1

Cancel the common factor of $5$ .

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Step 5.6.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{- \sqrt{19}}{5} + \frac{- 5}{5}$

Step 5.6.2.1.2

Divide $x$ by $1$ .

$x = \frac{- \sqrt{19}}{5} + \frac{- 5}{5}$

Step 5.6.3

Simplify the right side.

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Step 5.6.3.1

Simplify each term.

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Step 5.6.3.1.1

Move the negative in front of the fraction.

$x = - \frac{\sqrt{19}}{5} + \frac{- 5}{5}$

Step 5.6.3.1.2

Divide $- 5$ by $5$ .

$x = - \frac{\sqrt{19}}{5} - 1$

Step 5.7

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

$x = \frac{\sqrt{19}}{5} - 1, - \frac{\sqrt{19}}{5} - 1$

Step 6

The result can be shown in multiple forms.

Exact Form:

$x = \frac{\sqrt{19}}{5} - 1, - \frac{\sqrt{19}}{5} - 1$

Decimal Form:

$x = - 0.12822021 \dots, - 1.87177978 \dots$