Question

What is the expression in factored form x^2+13x+42

Answer 1

The correct answer is (x+6)(x+7). Great job.

Answer 2

we have

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

Find the factors

Equate the equation to zero

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

Group terms that contain the same variable, and move the constant to the opposite side of the equation

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

Complete the square. Remember to balance the equation by adding the same constants to each side

$x^{2} +13x+6.5^{2}=-42+6.5^{2}$

$x^{2} +13x+42.25=-42+42.25$

$x^{2} +13x+42.25=0.25$

Rewrite as perfect squares

$(x+6.5)^{2}=0.25$

Square root both sides

$(x+6.5)=(+/-)\sqrt{0.25} \\ \\x+6.5=(+/-)0.50 \\ \\x=-6.5(+/-) 0.50$

$x1=-6.5+0.50=-6$

$x2=-6.5-0.50=-7$

therefore

the answer is

$(x+6)(x+7)$