Question

How do you solve `x^2-8x=-10` using the quadratic formula?

Answer 1

`x=4+sqrt(11) or x=4-sqrt(11)`

Explanation:

Given
`color(white)("XXX")x^2-8x=-10`
Re-write in standard form:
`color(white)("XXX")color(red)1x^2color(blue)(-8)x+color(green)(10)=0`

The quadratic formula tells us that an equation of the form:
`color(white)("XXX")color(red)ax^2+color(blue)bx+color(green)c=0`
has solutions:
`color(white)("XXX")x=(-color(blue)b+-sqrt(color(blue)b-4color(red)acolor(green)c))/(2color(red)a`

So in this case the solutions are
`color(white)("XXX")x=(-(color(blue)(-8))+-sqrt((color(blue)(-8))^2-4xxcolor(red)1xxcolor(green)(10)))/(2xxcolor(red)1)`

`color(white)("XXXx")=(8+-sqrt(44))/2`

`color(white)("XXXx")=(8+-2sqrt(11))/2`

`color(white)("XXXx")=4+-sqrt(11)`