Pre-Algebra Examples

$9650 = x^{2} - 8 x + 62$

Step 1

Rewrite the equation as $x^{2} - 8 x + 62 = 9650$ .

$x^{2} - 8 x + 62 = 9650$

Step 2

Subtract $9650$ from both sides of the equation.

$x^{2} - 8 x + 62 - 9650 = 0$

Step 3

Subtract $9650$ from $62$ .

$x^{2} - 8 x - 9588 = 0$

Step 4

Factor $x^{2} - 8 x - 9588$ using the AC method.

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Step 4.1

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 $- 9588$ and whose sum is $- 8$ .

$- 102, 94$

Step 4.2

Write the factored form using these integers.

$(x - 102) (x + 94) = 0$

Step 5

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

$x - 102 = 0$

$x + 94 = 0$

Step 6

Set $x - 102$ equal to $0$ and solve for $x$ .

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Step 6.1

Set $x - 102$ equal to $0$ .

$x - 102 = 0$

Step 6.2

Add $102$ to both sides of the equation.

$x = 102$

Step 7

Set $x + 94$ equal to $0$ and solve for $x$ .

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Step 7.1

Set $x + 94$ equal to $0$ .

$x + 94 = 0$

Step 7.2

Subtract $94$ from both sides of the equation.

$x = - 94$

Step 8

The final solution is all the values that make $(x - 102) (x + 94) = 0$ true.

$x = 102, - 94$