Pre-Algebra Examples

$84 (x + 1) = (85 + x) (x - 1)$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$(85 + x) (x - 1) = 84 (x + 1)$

Step 2

Simplify $(85 + x) (x - 1)$ .

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Step 2.1

Rewrite.

$0 + 0 + (85 + x) (x - 1) = 84 (x + 1)$

Step 2.2

Simplify by adding zeros.

$(85 + x) (x - 1) = 84 (x + 1)$

Step 2.3

Expand $(85 + x) (x - 1)$ using the FOIL Method.

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Step 2.3.1

Apply the distributive property.

$85 (x - 1) + x (x - 1) = 84 (x + 1)$

Step 2.3.2

Apply the distributive property.

$85 x + 85 \cdot - 1 + x (x - 1) = 84 (x + 1)$

Step 2.3.3

Apply the distributive property.

$85 x + 85 \cdot - 1 + x \cdot x + x \cdot - 1 = 84 (x + 1)$

Step 2.4

Simplify and combine like terms.

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Step 2.4.1

Simplify each term.

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Step 2.4.1.1

Multiply $85$ by $- 1$ .

$85 x - 85 + x \cdot x + x \cdot - 1 = 84 (x + 1)$

Step 2.4.1.2

Multiply $x$ by $x$ .

$85 x - 85 + x^{2} + x \cdot - 1 = 84 (x + 1)$

Step 2.4.1.3

Move $- 1$ to the left of $x$ .

$85 x - 85 + x^{2} - 1 \cdot x = 84 (x + 1)$

Step 2.4.1.4

Rewrite $- 1 x$ as $- x$ .

$85 x - 85 + x^{2} - x = 84 (x + 1)$

Step 2.4.2

Subtract $x$ from $85 x$ .

$84 x - 85 + x^{2} = 84 (x + 1)$

Step 3

Simplify $84 (x + 1)$ .

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Step 3.1

Apply the distributive property.

$84 x - 85 + x^{2} = 84 x + 84 \cdot 1$

Step 3.2

Multiply $84$ by $1$ .

$84 x - 85 + x^{2} = 84 x + 84$

Step 4

Move all terms containing $x$ to the left side of the equation.

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Step 4.1

Subtract $84 x$ from both sides of the equation.

$84 x - 85 + x^{2} - 84 x = 84$

Step 4.2

Combine the opposite terms in $84 x - 85 + x^{2} - 84 x$ .

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Step 4.2.1

Subtract $84 x$ from $84 x$ .

$- 85 + x^{2} + 0 = 84$

Step 4.2.2

Add $- 85 + x^{2}$ and $0$ .

$- 85 + x^{2} = 84$

Step 5

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

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Step 5.1

Add $85$ to both sides of the equation.

$x^{2} = 84 + 85$

Step 5.2

Add $84$ and $85$ .

$x^{2} = 169$

Step 6

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

$x = \pm \sqrt{169}$

Step 7

Simplify $\pm \sqrt{169}$ .

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Step 7.1

Rewrite $169$ as $13^{2}$ .

$x = \pm \sqrt{13^{2}}$

Step 7.2

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

$x = \pm 13$

Step 8

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

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Step 8.1

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

$x = 13$

Step 8.2

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

$x = - 13$

Step 8.3

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

$x = 13, - 13$