Basic Math Examples

$(d - 5) (d + 5) = 39$

Step 1

Simplify $(d - 5) (d + 5)$ .

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Step 1.1

Expand $(d - 5) (d + 5)$ using the FOIL Method.

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Step 1.1.1

Apply the distributive property.

$d (d + 5) - 5 (d + 5) = 39$

Step 1.1.2

Apply the distributive property.

$d \cdot d + d \cdot 5 - 5 (d + 5) = 39$

Step 1.1.3

Apply the distributive property.

$d \cdot d + d \cdot 5 - 5 d - 5 \cdot 5 = 39$

Step 1.2

Simplify terms.

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Step 1.2.1

Combine the opposite terms in $d \cdot d + d \cdot 5 - 5 d - 5 \cdot 5$ .

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Step 1.2.1.1

Reorder the factors in the terms $d \cdot 5$ and $- 5 d$ .

$d \cdot d + 5 d - 5 d - 5 \cdot 5 = 39$

Step 1.2.1.2

Subtract $5 d$ from $5 d$ .

$d \cdot d + 0 - 5 \cdot 5 = 39$

Step 1.2.1.3

Add $d \cdot d$ and $0$ .

$d \cdot d - 5 \cdot 5 = 39$

Step 1.2.2

Simplify each term.

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Step 1.2.2.1

Multiply $d$ by $d$ .

$d^{2} - 5 \cdot 5 = 39$

Step 1.2.2.2

Multiply $- 5$ by $5$ .

$d^{2} - 25 = 39$

Step 2

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

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Step 2.1

Add $25$ to both sides of the equation.

$d^{2} = 39 + 25$

Step 2.2

Add $39$ and $25$ .

$d^{2} = 64$

Step 3

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

$d = \pm \sqrt{64}$

Step 4

Simplify $\pm \sqrt{64}$ .

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Step 4.1

Rewrite $64$ as $8^{2}$ .

$d = \pm \sqrt{8^{2}}$

Step 4.2

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

$d = \pm 8$

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.

$d = 8$

Step 5.2

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

$d = - 8$

Step 5.3

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

$d = 8, - 8$