Finite Math Examples

$160 x = 4200 + 30 x + x^{2}$

Step 1

Since $x$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$4200 + 30 x + x^{2} = 160 x$

Step 2

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

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Step 2.1

Subtract $160 x$ from both sides of the equation.

$4200 + 30 x + x^{2} - 160 x = 0$

Step 2.2

Subtract $160 x$ from $30 x$ .

$4200 + x^{2} - 130 x = 0$

Step 3

Factor $4200 + x^{2} - 130 x$ using the AC method.

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Step 3.1

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 $4200$ and whose sum is $- 130$ .

$- 70, - 60$

Step 3.2

Write the factored form using these integers.

$(x - 70) (x - 60) = 0$

Step 4

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

$x - 70 = 0$

$x - 60 = 0$

Step 5

Set $x - 70$ equal to $0$ and solve for $x$ .

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Step 5.1

Set $x - 70$ equal to $0$ .

$x - 70 = 0$

Step 5.2

Add $70$ to both sides of the equation.

$x = 70$

Step 6

Set $x - 60$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $x - 60$ equal to $0$ .

$x - 60 = 0$

Step 6.2

Add $60$ to both sides of the equation.

$x = 60$

Step 7

The final solution is all the values that make $(x - 70) (x - 60) = 0$ true.

$x = 70, 60$