Pre-Algebra Examples

$200 x - x^{2} = 40 x + 3375$

Step 1

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

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Step 1.1

Subtract $40 x$ from both sides of the equation.

$200 x - x^{2} - 40 x = 3375$

Step 1.2

Subtract $40 x$ from $200 x$ .

$- x^{2} + 160 x = 3375$

Step 2

Subtract $3375$ from both sides of the equation.

$- x^{2} + 160 x - 3375 = 0$

Step 3

Factor the left side of the equation.

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Step 3.1

Factor $- 1$ out of $- x^{2} + 160 x - 3375$ .

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Step 3.1.1

Factor $- 1$ out of $- x^{2}$ .

$- (x^{2}) + 160 x - 3375 = 0$

Step 3.1.2

Factor $- 1$ out of $160 x$ .

$- (x^{2}) - (- 160 x) - 3375 = 0$

Step 3.1.3

Rewrite $- 3375$ as $- 1 (3375)$ .

$- (x^{2}) - (- 160 x) - 1 \cdot 3375 = 0$

Step 3.1.4

Factor $- 1$ out of $- (x^{2}) - (- 160 x)$ .

$- (x^{2} - 160 x) - 1 \cdot 3375 = 0$

Step 3.1.5

Factor $- 1$ out of $- (x^{2} - 160 x) - 1 (3375)$ .

$- (x^{2} - 160 x + 3375) = 0$

Step 3.2

Factor.

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Step 3.2.1

Factor $x^{2} - 160 x + 3375$ using the AC method.

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Step 3.2.1.1

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 $3375$ and whose sum is $- 160$ .

$- 135, - 25$

Step 3.2.1.2

Write the factored form using these integers.

$- ((x - 135) (x - 25)) = 0$

Step 3.2.2

Remove unnecessary parentheses.

$- (x - 135) (x - 25) = 0$

Step 4

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

$x - 135 = 0$

$x - 25 = 0$

Step 5

Set $x - 135$ equal to $0$ and solve for $x$ .

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Step 5.1

Set $x - 135$ equal to $0$ .

$x - 135 = 0$

Step 5.2

Add $135$ to both sides of the equation.

$x = 135$

Step 6

Set $x - 25$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $x - 25$ equal to $0$ .

$x - 25 = 0$

Step 6.2

Add $25$ to both sides of the equation.

$x = 25$

Step 7

The final solution is all the values that make $- (x - 135) (x - 25) = 0$ true.

$x = 135, 25$