Question

How to change x² + 10x-8 to be written in the form (x + a)² + b

Answer 1

`\left(x+5\right)^2- 33=0`

See explanation below for steps

Explanation:

We are given the quadratic equation

`x^2+10x-8 = 0`

and asked to rewrite it in the form

`\left(x+a\right)^2=b`

Move 8 to the right side:

`x^2+10x=8`

`\mathrm{Rewrite\:in\:the\:form}\:x^2+2ax+a^2`

`\mathrm{Solve\:for\:}a,\:2ax=10x:\quad a=5`

`\mathrm{Add\:}a^2=5^2\mathrm{\:to\:both\:sides}`

`x^2+10x+5^2=8+5^2`

• 
  `x^2+10x+5^2= (x+5)^2`

• 
  `8+5^2 = 8 + 25 = 33`

So we get the original equation as:

`\left(x+5\right)^2=33`

which can be rewritten as

`\left(x+5\right)^2- 33=0`

Here a = 5, b = -33