Algebra Examples

$4 x^{2} - 64 = 8 x - 4$

Step 1

Move all the expressions to the left side of the equation.

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Step 1.1

Subtract $8 x$ from both sides of the equation.

$4 x^{2} - 64 - 8 x = - 4$

Step 1.2

Add $4$ to both sides of the equation.

$4 x^{2} - 64 - 8 x + 4 = 0$

Step 2

Add $- 64$ and $4$ .

$4 x^{2} - 8 x - 60 = 0$

Step 3

Factor $4$ out of $4 x^{2} - 8 x - 60$ .

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Step 3.1

Factor $4$ out of $4 x^{2}$ .

$4 (x^{2}) - 8 x - 60 = 0$

Step 3.2

Factor $4$ out of $- 8 x$ .

$4 (x^{2}) + 4 (- 2 x) - 60 = 0$

Step 3.3

Factor $4$ out of $- 60$ .

$4 x^{2} + 4 (- 2 x) + 4 \cdot - 15 = 0$

Step 3.4

Factor $4$ out of $4 x^{2} + 4 (- 2 x)$ .

$4 (x^{2} - 2 x) + 4 \cdot - 15 = 0$

Step 3.5

Factor $4$ out of $4 (x^{2} - 2 x) + 4 \cdot - 15$ .

$4 (x^{2} - 2 x - 15) = 0$

Step 4

Factor.

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Step 4.1

Factor $x^{2} - 2 x - 15$ using the AC method.

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Step 4.1.1

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 $- 15$ and whose sum is $- 2$ .

$- 5, 3$

Step 4.1.2

Write the factored form using these integers.

$4 ((x - 5) (x + 3)) = 0$

Step 4.2

Remove unnecessary parentheses.

$4 (x - 5) (x + 3) = 0$

Step 5

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

$x - 5 = 0$

$x + 3 = 0$

Step 6

Set $x - 5$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $x - 5$ equal to $0$ .

$x - 5 = 0$

Step 6.2

Add $5$ to both sides of the equation.

$x = 5$

Step 7

Set $x + 3$ equal to $0$ and solve for $x$ .

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Step 7.1

Set $x + 3$ equal to $0$ .

$x + 3 = 0$

Step 7.2

Subtract $3$ from both sides of the equation.

$x = - 3$

Step 8

The final solution is all the values that make $4 (x - 5) (x + 3) = 0$ true.

$x = 5, - 3$