Pre-Algebra Examples

$5 x^{2} - x - 50 = 2 (2 x^{2} + 3)$

Step 1

Simplify $2 (2 x^{2} + 3)$ .

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Step 1.1

Rewrite.

$5 x^{2} - x - 50 = 0 + 0 + 2 (2 x^{2} + 3)$

Step 1.2

Simplify by adding zeros.

$5 x^{2} - x - 50 = 2 (2 x^{2} + 3)$

Step 1.3

Apply the distributive property.

$5 x^{2} - x - 50 = 2 (2 x^{2}) + 2 \cdot 3$

Step 1.4

Multiply.

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Step 1.4.1

Multiply $2$ by $2$ .

$5 x^{2} - x - 50 = 4 x^{2} + 2 \cdot 3$

Step 1.4.2

Multiply $2$ by $3$ .

$5 x^{2} - x - 50 = 4 x^{2} + 6$

Step 2

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

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Step 2.1

Subtract $4 x^{2}$ from both sides of the equation.

$5 x^{2} - x - 50 - 4 x^{2} = 6$

Step 2.2

Subtract $4 x^{2}$ from $5 x^{2}$ .

$x^{2} - x - 50 = 6$

Step 3

Subtract $6$ from both sides of the equation.

$x^{2} - x - 50 - 6 = 0$

Step 4

Subtract $6$ from $- 50$ .

$x^{2} - x - 56 = 0$

Step 5

Factor $x^{2} - x - 56$ using the AC method.

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Step 5.1

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 56$ and whose sum is $- 1$ .

$- 8, 7$

Step 5.2

Write the factored form using these integers.

$(x - 8) (x + 7) = 0$

Step 6

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x - 8 = 0$

$x + 7 = 0$

Step 7

Set $x - 8$ equal to $0$ and solve for $x$ .

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Step 7.1

Set $x - 8$ equal to $0$ .

$x - 8 = 0$

Step 7.2

Add $8$ to both sides of the equation.

$x = 8$

Step 8

Set $x + 7$ equal to $0$ and solve for $x$ .

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Step 8.1

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

$x + 7 = 0$

Step 8.2

Subtract $7$ from both sides of the equation.

$x = - 7$

Step 9

The final solution is all the values that make $(x - 8) (x + 7) = 0$ true.

$x = 8, - 7$