Finite Math Examples

$15000 - 500 x + 4 {(x)}^{2} = 0$

Step 1

Factor the left side of the equation.

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Step 1.1

Factor $4$ out of $15000 - 500 x + 4 x^{2}$ .

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Step 1.1.1

Factor $4$ out of $15000$ .

$4 \cdot 3750 - 500 x + 4 x^{2} = 0$

Step 1.1.2

Factor $4$ out of $- 500 x$ .

$4 \cdot 3750 + 4 (- 125 x) + 4 x^{2} = 0$

Step 1.1.3

Factor $4$ out of $4 \cdot 3750 + 4 (- 125 x)$ .

$4 \cdot (3750 - 125 x) + 4 x^{2} = 0$

Step 1.1.4

Factor $4$ out of $4 \cdot (3750 - 125 x) + 4 x^{2}$ .

$4 (3750 - 125 x + x^{2}) = 0$

Step 1.2

Factor.

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Step 1.2.1

Factor $3750 - 125 x + x^{2}$ using the AC method.

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Step 1.2.1.1

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 $3750$ and whose sum is $- 125$ .

$- 75, - 50$

Step 1.2.1.2

Write the factored form using these integers.

$4 ((x - 75) (x - 50)) = 0$

Step 1.2.2

Remove unnecessary parentheses.

$4 (x - 75) (x - 50) = 0$

Step 2

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

$x - 75 = 0$

$x - 50 = 0$

Step 3

Set $x - 75$ equal to $0$ and solve for $x$ .

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Step 3.1

Set $x - 75$ equal to $0$ .

$x - 75 = 0$

Step 3.2

Add $75$ to both sides of the equation.

$x = 75$

Step 4

Set $x - 50$ equal to $0$ and solve for $x$ .

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Step 4.1

Set $x - 50$ equal to $0$ .

$x - 50 = 0$

Step 4.2

Add $50$ to both sides of the equation.

$x = 50$

Step 5

The final solution is all the values that make $4 (x - 75) (x - 50) = 0$ true.

$x = 75, 50$