# 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) #