Question

x^2-x- 18 = 4 how do I solve for all values of x by factoring

Answer 1

We are given the following equation

$x^2-x-18=-4x$

We are asked to solve for x by factoring the equation

Let us first simplify the equation

$\begin{gathered} x^2-x-18=-4x \\ x^2-x+4x-18=0 \\ x^2+3x-18=0 \end{gathered}$

The equation has been simplified and now we can proceed to factor this equation

The standard form of a quadratic equation is given by

$Ax^2+Bx+C=0$

Comparing the standard form with our equation we see that

A = 1

B = 3

C = -18

Now to factor the equation, we need to think about two numbers such that

When we multiply them, we get A×C = -18

When we add them, we get B = 3

Can you think of such two numbers?

How about 6 and -3?

When we multiply them we get, 6×-3 = -18 (satisfied)

When we add them together we get, 6 +(-3) = 3 (satisfied)

So, our equation becomes

$\begin{gathered} x^2+6x-3x-18 \\ x\mleft(x+6\mright)-3\mleft(x+6\mright) \\ \mleft(x+6\mright)\mleft(x-3\mright)_{} \end{gathered}$

The above equation is the factorized equation.

Now let us solve for x

x + 6 = 0

x = -6

x - 3 = 0

x = 3

Therefore, the solutions of the given quadratic equation are x = (-6, 3)