Algebra Examples

${(x + 7)}^{2} = x^{2} + 14 x + 49$

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.

$x^{2} + 14 x + 49 = {(x + 7)}^{2}$

Step 2

Simplify ${(x + 7)}^{2}$ .

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Step 2.1

Rewrite.

$x^{2} + 14 x + 49 = 0 + 0 + {(x + 7)}^{2}$

Step 2.2

Rewrite ${(x + 7)}^{2}$ as $(x + 7) (x + 7)$ .

$x^{2} + 14 x + 49 = (x + 7) (x + 7)$

Step 2.3

Expand $(x + 7) (x + 7)$ using the FOIL Method.

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Step 2.3.1

Apply the distributive property.

$x^{2} + 14 x + 49 = x (x + 7) + 7 (x + 7)$

Step 2.3.2

Apply the distributive property.

$x^{2} + 14 x + 49 = x \cdot x + x \cdot 7 + 7 (x + 7)$

Step 2.3.3

Apply the distributive property.

$x^{2} + 14 x + 49 = x \cdot x + x \cdot 7 + 7 x + 7 \cdot 7$

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 $x$ by $x$ .

$x^{2} + 14 x + 49 = x^{2} + x \cdot 7 + 7 x + 7 \cdot 7$

Step 2.4.1.2

Move $7$ to the left of $x$ .

$x^{2} + 14 x + 49 = x^{2} + 7 \cdot x + 7 x + 7 \cdot 7$

Step 2.4.1.3

Multiply $7$ by $7$ .

$x^{2} + 14 x + 49 = x^{2} + 7 x + 7 x + 49$

Step 2.4.2

Add $7 x$ and $7 x$ .

$x^{2} + 14 x + 49 = x^{2} + 14 x + 49$

Step 3

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

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Step 3.1

Subtract $x^{2}$ from both sides of the equation.

$x^{2} + 14 x + 49 - x^{2} = 14 x + 49$

Step 3.2

Subtract $14 x$ from both sides of the equation.

$x^{2} + 14 x + 49 - x^{2} - 14 x = 49$

Step 3.3

Combine the opposite terms in $x^{2} + 14 x + 49 - x^{2} - 14 x$ .

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Step 3.3.1

Subtract $x^{2}$ from $x^{2}$ .

$14 x + 49 + 0 - 14 x = 49$

Step 3.3.2

Add $14 x + 49$ and $0$ .

$14 x + 49 - 14 x = 49$

Step 3.3.3

Subtract $14 x$ from $14 x$ .

$0 + 49 = 49$

Step 3.3.4

Add $0$ and $49$ .

$49 = 49$

Step 4

Since $49 = 49$ , the equation will always be true for any value of $x$ .

All real numbers

Step 5

The result can be shown in multiple forms.

All real numbers

Interval Notation:

$(- \infty, \infty)$