Algebra Examples

$3 {(y + 1)}^{2} - 5 = 43$

Step 1

Add $5$ to both sides of the equation.

$3 {(y + 1)}^{2} = 43 + 5$

Step 2

Add $43$ and $5$ .

$3 {(y + 1)}^{2} = 48$

Step 3

Divide each term in $3 {(y + 1)}^{2} = 48$ by $3$ and simplify.

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Step 3.1

Divide each term in $3 {(y + 1)}^{2} = 48$ by $3$ .

$\frac{3 {(y + 1)}^{2}}{3} = \frac{48}{3}$

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.

$\frac{3 {(y + 1)}^{2}}{3} = \frac{48}{3}$

Step 3.2.1.2

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

${(y + 1)}^{2} = \frac{48}{3}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $48$ by $3$ .

${(y + 1)}^{2} = 16$

Step 4

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

$y + 1 = \pm \sqrt{16}$

Step 5

Simplify $\pm \sqrt{16}$ .

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Step 5.1

Rewrite $16$ as $4^{2}$ .

$y + 1 = \pm \sqrt{4^{2}}$

Step 5.2

Pull terms out from under the radical, assuming positive real numbers.

$y + 1 = \pm 4$

Step 6

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

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Step 6.1

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

$y + 1 = 4$

Step 6.2

Move all terms not containing $y$ to the right side of the equation.

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Step 6.2.1

Subtract $1$ from both sides of the equation.

$y = 4 - 1$

Step 6.2.2

Subtract $1$ from $4$ .

$y = 3$

Step 6.3

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

$y + 1 = - 4$

Step 6.4

Move all terms not containing $y$ to the right side of the equation.

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Step 6.4.1

Subtract $1$ from both sides of the equation.

$y = - 4 - 1$

Step 6.4.2

Subtract $1$ from $- 4$ .

$y = - 5$

Step 6.5

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

$y = 3, - 5$