SOLUTION: Solve the equation: -x^2+4=2x^2-5

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Question 548465: Solve the equation: -x^2+4=2x^2-5
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

-x%5E2%2B4=2x%5E2-5 Start with the given equation.


-x%5E2%2B4-2x%5E2%2B5=0 Get every term to the left side.


-3x%5E2%2B9=0 Combine like terms.


Notice that the quadratic -3x%5E2%2B9 is in the form of Ax%5E2%2BBx%2BC where A=-3, B=0, 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-%280%29+%2B-+sqrt%28+%280%29%5E2-4%28-3%29%289%29+%29%29%2F%282%28-3%29%29 Plug in A=-3, B=0, and C=9


x+=+%28-0+%2B-+sqrt%28+0-4%28-3%29%289%29+%29%29%2F%282%28-3%29%29 Square 0 to get 0.


x+=+%28-0+%2B-+sqrt%28+0--108+%29%29%2F%282%28-3%29%29 Multiply 4%28-3%29%289%29 to get -108


x+=+%28-0+%2B-+sqrt%28+0%2B108+%29%29%2F%282%28-3%29%29 Rewrite sqrt%280--108%29 as sqrt%280%2B108%29


x+=+%28-0+%2B-+sqrt%28+108+%29%29%2F%282%28-3%29%29 Add 0 to 108 to get 108


x+=+%28-0+%2B-+sqrt%28+108+%29%29%2F%28-6%29 Multiply 2 and -3 to get -6.


x+=+%28-0+%2B-+6%2Asqrt%283%29%29%2F%28-6%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-0%29%2F%28-6%29+%2B-+%286%2Asqrt%283%29%29%2F%28-6%29 Break up the fraction.


x+=+0+%2B-+-1%2Asqrt%283%29 Reduce.


x+=+0-1%2Asqrt%283%29 or x+=+0%2B1%2Asqrt%283%29 Break up the expression.


So the solutions are x+=+-sqrt%283%29 or x+=+sqrt%283%29