Pre-Algebra Examples

$x^{2} + 18 x = 4 x - 49$

Step 1

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

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Step 1.1

Subtract $4 x$ from both sides of the equation.

$x^{2} + 18 x - 4 x = - 49$

Step 1.2

Subtract $4 x$ from $18 x$ .

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

Step 2

Add $49$ to both sides of the equation.

$x^{2} + 14 x + 49 = 0$

Step 3

Factor using the perfect square rule.

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Step 3.1

Rewrite $49$ as $7^{2}$ .

$x^{2} + 14 x + 7^{2} = 0$

Step 3.2

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$14 x = 2 \cdot x \cdot 7$

Step 3.3

Rewrite the polynomial.

$x^{2} + 2 \cdot x \cdot 7 + 7^{2} = 0$

Step 3.4

Factor using the perfect square trinomial rule $a^{2} + 2 a b + b^{2} = {(a + b)}^{2}$ , where $a = x$ and $b = 7$ .

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

Step 4

Set the $x + 7$ equal to $0$ .

$x + 7 = 0$

Step 5

Subtract $7$ from both sides of the equation.

$x = - 7$