Question

How do you use the quadratic formula to solve `2(x-3)^2=-2x+9`?

Answer 1

`x = 5/2 +- 1/2sqrt(7)`

Explanation:

We can use the quadratic formula:

`x = (-b +- sqrt(b^2-4ac))/(2a)`

to solve a quadratic equation of the form:

`ax^2 + bx + c =0`

So as we have:

`2(x-3)^2 = -2x + 9`

The first thing we should do is expand the expression and rearrange into standard form:

`:. 2(x-3)(x-3) = -2x + 9`
`:. 2(x^2-3x-3x+9) = -2x + 9`
`:. 2x^2-12x+18 = -2x + 9`
`:. 2x^2-10x+9 = 0`

We can now apply the quadratic formula:

`x = (-(-10) +- sqrt( (-10)^2-4(2)(9)))/(2(2))`
`\ \ = (10 +- sqrt( 100-72))/(4)`
`\ \ = (10 +- sqrt( 28))/(4)`
`\ \ = (10 +- 2sqrt(7))/(4)`
`\ \ = 5/2 +- 1/2sqrt(7)`