SOLUTION: (x-3)(x-2)=(x+5)(2x-3)+21 Solve for the negative value of X.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: (x-3)(x-2)=(x+5)(2x-3)+21 Solve for the negative value of X.      Log On


   

Question 211462: (x-3)(x-2)=(x+5)(2x-3)+21 Solve for the negative value of X.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-3%29%28x-2%29=%28x%2B5%29%282x-3%29%2B21 Start with the given equation.


x%5E2-5x%2B6=2x%5E2%2B7x-15%2B21 FOIL


x%5E2-5x%2B6=2x%5E2%2B7x%2B6 Combine like terms.


x%5E2-5x%2B6-2x%5E2-7x-6=0 Get every term to the left side.


-x%5E2-12x=0 Combine like terms.


Notice that the quadratic -x%5E2-12x%2B0 is in the form of Ax%5E2%2BBx%2BC where A=-1, B=-12, and C=0


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-%28-12%29+%2B-+sqrt%28+%28-12%29%5E2-4%28-1%29%280%29+%29%29%2F%282%28-1%29%29 Plug in A=-1, B=-12, and C=0


x+=+%2812+%2B-+sqrt%28+%28-12%29%5E2-4%28-1%29%280%29+%29%29%2F%282%28-1%29%29 Negate -12 to get 12.


x+=+%2812+%2B-+sqrt%28+144-4%28-1%29%280%29+%29%29%2F%282%28-1%29%29 Square -12 to get 144.


x+=+%2812+%2B-+sqrt%28+144-0+%29%29%2F%282%28-1%29%29 Multiply 4%28-1%29%280%29 to get 0


x+=+%2812+%2B-+sqrt%28+144+%29%29%2F%282%28-1%29%29 Subtract 0 from 144 to get 144


x+=+%2812+%2B-+sqrt%28+144+%29%29%2F%28-2%29 Multiply 2 and -1 to get -2.


x+=+%2812+%2B-+12%29%2F%28-2%29 Take the square root of 144 to get 12.


x+=+%2812+%2B+12%29%2F%28-2%29 or x+=+%2812+-+12%29%2F%28-2%29 Break up the expression.


x+=+%2824%29%2F%28-2%29 or x+=++%280%29%2F%28-2%29 Combine like terms.


x+=+-12 or x+=+0 Simplify.


So the solutions are x+=+-12 or x+=+0