Pre-Algebra Examples

$34 = (x + 3) + (x + 6) + (x^{2} - 2 x) + (3 x - 3)$

Step 1

Rewrite the equation as $x + 3 + x + 6 + x^{2} - 2 x + 3 x - 3 = 34$ .

$x + 3 + x + 6 + x^{2} - 2 x + 3 x - 3 = 34$

Step 2

Simplify $x + 3 + x + 6 + x^{2} - 2 x + 3 x - 3$ .

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Step 2.1

Combine the opposite terms in $x + 3 + x + 6 + x^{2} - 2 x + 3 x - 3$ .

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Step 2.1.1

Subtract $3$ from $3$ .

$x + x + 6 + x^{2} - 2 x + 3 x + 0 = 34$

Step 2.1.2

Add $x + x + 6 + x^{2} - 2 x + 3 x$ and $0$ .

$x + x + 6 + x^{2} - 2 x + 3 x = 34$

Step 2.2

Add $x$ and $x$ .

$2 x + 6 + x^{2} - 2 x + 3 x = 34$

Step 2.3

Combine the opposite terms in $2 x + 6 + x^{2} - 2 x + 3 x$ .

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Step 2.3.1

Subtract $2 x$ from $2 x$ .

$6 + x^{2} + 0 + 3 x = 34$

Step 2.3.2

Add $6 + x^{2}$ and $0$ .

$6 + x^{2} + 3 x = 34$

Step 3

Subtract $34$ from both sides of the equation.

$6 + x^{2} + 3 x - 34 = 0$

Step 4

Subtract $34$ from $6$ .

$x^{2} + 3 x - 28 = 0$

Step 5

Factor $x^{2} + 3 x - 28$ 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 $- 28$ and whose sum is $3$ .

$- 4, 7$

Step 5.2

Write the factored form using these integers.

$(x - 4) (x + 7) = 0$

Step 6

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

$x - 4 = 0$

$x + 7 = 0$

Step 7

Set $x - 4$ equal to $0$ and solve for $x$ .

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Step 7.1

Set $x - 4$ equal to $0$ .

$x - 4 = 0$

Step 7.2

Add $4$ to both sides of the equation.

$x = 4$

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 $(x - 4) (x + 7) = 0$ true.

$x = 4, - 7$