How do you use the quadratic formula to solve 2(x-3)^2=-2x+9?
1 Answer
May 14, 2017
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)
