Solve by Factoring x^2+13x+43=1

$x^{2} + 13 x + 43 = 1$

Step 1

Subtract $1$ from both sides of the equation.

$x^{2} + 13 x + 43 - 1 = 0$

Step 2

Subtract $1$ from $43$ .

$x^{2} + 13 x + 42 = 0$

Step 3

Factor $x^{2} + 13 x + 42$ 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 $42$ and whose sum is $13$ .

$6, 7$

Write the factored form using these integers.

$(x + 6) (x + 7) = 0$

Step 4

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

$x + 6 = 0$

$x + 7 = 0$

Step 5

Set $x + 6$ equal to $0$ and solve for $x$ .

Set $x + 6$ equal to $0$ .

$x + 6 = 0$

Subtract $6$ from both sides of the equation.

$x = - 6$

Step 6

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

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

$x + 7 = 0$

Subtract $7$ from both sides of the equation.

$x = - 7$

Step 7

The final solution is all the values that make $(x + 6) (x + 7) = 0$ true.

$x = - 6, - 7$

Solve by Factoring x^2+13x+43=1

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