SOLUTION: Use the quadratic formula to solve the equation. 2(x-3)^2=-2x+9

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Use the quadratic formula to solve the equation. 2(x-3)^2=-2x+9      Log On


   

Question 172426: Use the quadratic formula to solve the equation.
2(x-3)^2=-2x+9
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
2%28x-3%29%5E2=-2x%2B9 Start with the given equation.


2%28x%5E2-6x%2B9%29=-2x%2B9 FOIL


2x%5E2-12x%2B18=-2x%2B9 Distribute


2x%5E2-12x%2B18%2B2x-9=0 Get all terms to the left side.


2x%5E2-10x%2B9=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=-10, and c=9


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%28-10%29+%2B-+sqrt%28+%28-10%29%5E2-4%282%29%289%29+%29%29%2F%282%282%29%29 Plug in a=2, b=-10, and c=9


x+=+%2810+%2B-+sqrt%28+%28-10%29%5E2-4%282%29%289%29+%29%29%2F%282%282%29%29 Negate -10 to get 10.


x+=+%2810+%2B-+sqrt%28+100-4%282%29%289%29+%29%29%2F%282%282%29%29 Square -10 to get 100.


x+=+%2810+%2B-+sqrt%28+100-72+%29%29%2F%282%282%29%29 Multiply 4%282%29%289%29 to get 72


x+=+%2810+%2B-+sqrt%28+28+%29%29%2F%282%282%29%29 Subtract 72 from 100 to get 28


x+=+%2810+%2B-+sqrt%28+28+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%2810+%2B-+2%2Asqrt%287%29%29%2F%284%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%2810%2B2%2Asqrt%287%29%29%2F%284%29 or x+=+%2810-2%2Asqrt%287%29%29%2F%284%29 Break up the expression.


So the answers are x+=+%2810%2B2%2Asqrt%287%29%29%2F%284%29 or x+=+%2810-2%2Asqrt%287%29%29%2F%284%29


which approximate to x=3.823 or x=1.177