Solve by Factoring x^2+61=1-17x

$x^{2} + 61 = 1 - 17 x$

Step 1

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

Subtract $1$ from both sides of the equation.

$x^{2} + 61 - 1 = - 17 x$

Add $17 x$ to both sides of the equation.

$x^{2} + 61 - 1 + 17 x = 0$

Step 2

Subtract $1$ from $61$ .

$x^{2} + 60 + 17 x = 0$

Step 3

Factor $x^{2} + 60 + 17 x$ 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 $60$ and whose sum is $17$ .

$5, 12$

Write the factored form using these integers.

$(x + 5) (x + 12) = 0$

Step 4

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

$x + 5 = 0$

$x + 12 = 0$

Step 5

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 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 $(x + 5) (x + 12) = 0$ true.

$x = - 5, - 12$

Solve by Factoring x^2+61=1-17x

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