Question

Solve this equation for x: x^2+11x+28=0

Answer 1

Answer: x = -7 or x = -4

Step-by-step explanation: When an equation has a squared term in it

such as x² + 11x + 28 = 0, it's called a polynomial equation.

The rule for solving a polynomial equation

is to first set it equal to zero, then factor.

Since this equation is already set equal to zero,

our first step is to factor the left side of the equation.

To factor x² + 11x + 28, we need the factors

of 28 that add to 11 which are 7 and 4.

So we have (x + 7)(x + 4) = 0.

Whenever two terms are multiplied together to equal zero,

this means that either one or the other must equal zero.

So if (x + 7)(x + 4) = 0, then either x + 7 = 0 or x + 4 = 0.

Solving each equation from here, we get x = -7 or x = -4.

So our solution is {-7, -4}.