SOLUTION: Solve for x. Simplify 4x^2 -5=-21

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Question 559911: Solve for x. Simplify 4x^2 -5=-21
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E2-5=-21 Start with the given equation.


4x%5E2-5%2B21=0 Get every term to the left side.


4x%5E2%2B16=0 Combine like terms.


Notice that the quadratic 4x%5E2%2B16 is in the form of Ax%5E2%2BBx%2BC where A=4, B=0, and C=16


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%284%29%2816%29+%29%29%2F%282%284%29%29 Plug in A=4, B=0, and C=16


x+=+%28-0+%2B-+sqrt%28+0-4%284%29%2816%29+%29%29%2F%282%284%29%29 Square 0 to get 0.


x+=+%28-0+%2B-+sqrt%28+0-256+%29%29%2F%282%284%29%29 Multiply 4%284%29%2816%29 to get 256


x+=+%28-0+%2B-+sqrt%28+-256+%29%29%2F%282%284%29%29 Subtract 256 from 0 to get -256


x+=+%28-0+%2B-+sqrt%28+-256+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%28-0+%2B-+16%2Ai%29%2F%288%29 Take the square root of -256 to get 16%2Ai.


x+=+%28-0+%2B+16%2Ai%29%2F%288%29 or x+=+%28-0+-+16%2Ai%29%2F%288%29 Break up the expression.


x+=+%28-0%29%2F%288%29+%2B+%2816%2Ai%29%2F%288%29 or x+=++%28-0%29%2F%288%29+-+%2816%2Ai%29%2F%288%29 Break up the fraction for each case.


x+=+0%2B2%2Ai or x+=++0-2%2Ai Reduce.


x+=+2%2Ai or x+=+-2%2Ai Simplify.


So the solutions are x+=+2%2Ai or x+=+-2%2Ai
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