Question

`{x }^(2) + 13 + 40 = 0`solve the equation show your reasoning

Answer 1

To solve the quadratic equation, we must factorize the left side into two factors

`x^2+13x+40=0`

We have to look for two numbers their product = 40, and their sum = 13

Since 8 x 5 = 40 and 8 + 5 = 13, then the factors will be

(x + 5) and (x + 8)

`\begin{gathered} x^2+13x+40=(x+5)(x+8) \\ (x+5)(x+8)=0 \end{gathered}`

Now we will equate each factor by 0

`\begin{gathered} x+5=0 \\ x+8=0 \end{gathered}`

Let us solve them to find the values of x

x + 5 = 0

Subtract 5 from both sides

`\begin{gathered} x+5-5=0-5 \\ x=-5 \end{gathered}`

x + 8 = 0

Subtract 8 from both sides

`\begin{gathered} x+8-8=0-8 \\ x=-8 \end{gathered}`

The solution of the equation is

x = -5 and x = -8

The answer is

x = -5 and x = -8