Finite Math Examples

$6 - x = x^{2} - 8 x + 16$

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.

$x^{2} - 8 x + 16 = 6 - x$

Step 2

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

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Step 2.1

Add $x$ to both sides of the equation.

$x^{2} - 8 x + 16 + x = 6$

Step 2.2

Add $- 8 x$ and $x$ .

$x^{2} - 7 x + 16 = 6$

Step 3

Subtract $6$ from both sides of the equation.

$x^{2} - 7 x + 16 - 6 = 0$

Step 4

Subtract $6$ from $16$ .

$x^{2} - 7 x + 10 = 0$

Step 5

Factor $x^{2} - 7 x + 10$ 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 $10$ and whose sum is $- 7$ .

$- 5, - 2$

Step 5.2

Write the factored form using these integers.

$(x - 5) (x - 2) = 0$

Step 6

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

$x - 5 = 0$

$x - 2 = 0$

Step 7

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

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Step 7.1

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

$x - 5 = 0$

Step 7.2

Add $5$ to both sides of the equation.

$x = 5$

Step 8

Set $x - 2$ equal to $0$ and solve for $x$ .

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Step 8.1

Set $x - 2$ equal to $0$ .

$x - 2 = 0$

Step 8.2

Add $2$ to both sides of the equation.

$x = 2$

Step 9

The final solution is all the values that make $(x - 5) (x - 2) = 0$ true.

$x = 5, 2$