Solve by Factoring x^2+9x-83=4x+1

$x^{2} + 9 x - 83 = 4 x + 1$

Step 1

Move all the expressions to the left side of the equation.

Subtract $4 x$ from both sides of the equation.

$x^{2} + 9 x - 83 - 4 x = 1$

Subtract $1$ from both sides of the equation.

$x^{2} + 9 x - 83 - 4 x - 1 = 0$

Step 2

Simplify $x^{2} + 9 x - 83 - 4 x - 1$ .

Subtract $4 x$ from $9 x$ .

$x^{2} + 5 x - 83 - 1 = 0$

Subtract $1$ from $- 83$ .

$x^{2} + 5 x - 84 = 0$

Step 3

Factor $x^{2} + 5 x - 84$ using the AC method.

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 $- 84$ and whose sum is $5$ .

$- 7, 12$

Write the factored form using these integers.

$(x - 7) (x + 12) = 0$

Step 4

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

$x - 7 = 0$

$x + 12 = 0$

Step 5

Set $x - 7$ equal to $0$ and solve for $x$ .

Set $x - 7$ equal to $0$ .

$x - 7 = 0$

Add $7$ to both sides of the equation.

$x = 7$

Step 6

Set $x + 12$ equal to $0$ and solve for $x$ .

Set $x + 12$ equal to $0$ .

$x + 12 = 0$

Subtract $12$ from both sides of the equation.

$x = - 12$

Step 7

The final solution is all the values that make $(x - 7) (x + 12) = 0$ true.

$x = 7, - 12$

Solve by Factoring x^2+9x-83=4x+1

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