Solve by Factoring x^2-x-46=3x-1

$x^{2} - x - 46 = 3 x - 1$

Step 1

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

Subtract $3 x$ from both sides of the equation.

$x^{2} - x - 46 - 3 x = - 1$

Add $1$ to both sides of the equation.

$x^{2} - x - 46 - 3 x + 1 = 0$

Step 2

Simplify $x^{2} - x - 46 - 3 x + 1$ .

Subtract $3 x$ from $- x$ .

$x^{2} - 4 x - 46 + 1 = 0$

Add $- 46$ and $1$ .

$x^{2} - 4 x - 45 = 0$

Step 3

Factor $x^{2} - 4 x - 45$ 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 $- 45$ and whose sum is $- 4$ .

$- 9, 5$

Write the factored form using these integers.

$(x - 9) (x + 5) = 0$

Step 4

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

$x - 9 = 0$

$x + 5 = 0$

Step 5

Set $x - 9$ equal to $0$ and solve for $x$ .

Set $x - 9$ equal to $0$ .

$x - 9 = 0$

Add $9$ to both sides of the equation.

$x = 9$

Step 6

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

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

$x + 5 = 0$

Subtract $5$ from both sides of the equation.

$x = - 5$

Step 7

The final solution is all the values that make $(x - 9) (x + 5) = 0$ true.

$x = 9, - 5$

Solve by Factoring x^2-x-46=3x-1

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