Respuesta :
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:
[tex]x=16\text{ or }x=-2[/tex]
Step-by-step explanation:
We have been given a quadratic equation and we are asked to solve for x.
[tex]x^{2}-14x+31=63[/tex]
Let us subtract 63 from both sides of our equation.
[tex]x^{2}-14x+31-63=63-63[/tex]
[tex]x^{2}-14x-32=0[/tex]
Now we will factor our given quadratic equation by splitting the middle term.
[tex]x^{2}-16x+2x-32=0[/tex]
[tex]x(x-16)+2(x-16)=0[/tex]
[tex](x-16)(x+2)=0[/tex]
[tex](x-16)=0\text{ or }(x+2)=0[/tex]
[tex]x-16+16=0+16\text{ or }x+2-2=0-2[/tex]
[tex]x=16\text{ or }x=-2[/tex]
Therefore, our quadratic equation has two solutions.
