Question

Solve each equation by completing the square. x^2–10x=13

Answer 1

`x^2-10x=13\rightarrow x^2-10x-13=0`
`(x+a)^2=\text{ (x+a)}\cdot(x+a)=x(x+a)+a(x+a)=x^2+ax+ax+a^2=x^2+2ax+a^2`

We need to adjust our equation in such way, that it follows the square pattern.

`2a=-10\rightarrow a\text{ = -5, }`

This also says that the last term should be 25, so by adding 38 on both sides , we get following.

`x^2-10x=13\rightarrow x^2-10x+25=38`
`(x-5)^2=38\rightarrow x\text{ = }\sqrt[]{38}+5`