Question

Solve x2 – 14x + 31 = 63 for x.

Answer 1

Step 1: Subtract 63 from both sides.x2−14x+31−63=63−63x2−14x−32=0Step 2: Factor left side of equation.(x+2)(x−16)=0Step 3: Set factors equal to 0.x+2=0 or x−16=0x=−2 or x=16Answer:x=−2 or x=16

Answer 2

`x=16\text{ or }x=-2`

Explanation:

We have been given a quadratic equation and we are asked to solve for x.

`x^(2)-14x+31=63`

Let us subtract 63 from both sides of our equation.

`x^(2)-14x+31-63=63-63`

`x^(2)-14x-32=0`

Now we will factor our given quadratic equation by splitting the middle term.

`x^(2)-16x+2x-32=0`

`x(x-16)+2(x-16)=0`

`(x-16)(x+2)=0`

`(x-16)=0\text{ or }(x+2)=0`

`x-16+16=0+16\text{ or }x+2-2=0-2`

`x=16\text{ or }x=-2`

Therefore, our quadratic equation has two solutions.