Question

Solve by factoring: x^2- 13х – 14 = 0 А. x = -14, х = 1 В. x = -1, x= 14 с. x=-7, х = 2 D. х = -2, х = 7

Answer 1

Step 1

Given;

`x^2-13x-14=0`

Required: To solve by factoring.

Step 2

Solve the equation by factoring

`\begin{gathered} Find\text{ the factors that will give you;} \\ 1)(-13x)\text{ when added} \\ 2)-14x^2\text{ when multiplied} \\ \text{These factors are; -14x and x} \end{gathered}`

Replace -13x with (-14x+x)

`x^2-14x+x-14=0`
`\begin{gathered} \text{Factorize the problem} \\ (x^2-14x)(+x-14)=0 \\ x((x^2)/(x)-(14x)/(x))+1(x-14)=0 \\ x(x-14)+1(x-14)=0 \end{gathered}`
`\begin{gathered} (x+1)(x-14)=0 \\ x+1=0 \\ or \\ x-14=0 \\ x=-1 \\ or \\ x=14 \end{gathered}`

Hence, the answer is x=14 or x = -1 . Option