SOLUTION: 4x2+20x+25=-2

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Question 297081: 4x2+20x+25=-2
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E2%2B20x%2B25=-2 Start with the given equation.


4x%5E2%2B20x%2B25%2B2=0 Add 2 to both sides.


4x%5E2%2B20x%2B27=0 Combine like terms.


Notice that the quadratic 4x%5E2%2B20x%2B27 is in the form of Ax%5E2%2BBx%2BC where A=4, B=20, and C=27


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-%2820%29+%2B-+sqrt%28+%2820%29%5E2-4%284%29%2827%29+%29%29%2F%282%284%29%29 Plug in A=4, B=20, and C=27


x+=+%28-20+%2B-+sqrt%28+400-4%284%29%2827%29+%29%29%2F%282%284%29%29 Square 20 to get 400.


x+=+%28-20+%2B-+sqrt%28+400-432+%29%29%2F%282%284%29%29 Multiply 4%284%29%2827%29 to get 432


x+=+%28-20+%2B-+sqrt%28+-32+%29%29%2F%282%284%29%29 Subtract 432 from 400 to get -32


x+=+%28-20+%2B-+sqrt%28+-32+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%28-20+%2B-+4i%2Asqrt%282%29%29%2F%288%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-20%2B4i%2Asqrt%282%29%29%2F%288%29 or x+=+%28-20-4i%2Asqrt%282%29%29%2F%288%29 Break up the expression.


x+=+%28-5%2Bi%2Asqrt%282%29%29%2F%282%29 or x+=+%28-5-i%2Asqrt%282%29%29%2F%282%29 Reduce.


So the solutions are x+=+%28-5%2Bi%2Asqrt%282%29%29%2F%282%29 or x+=+%28-5-i%2Asqrt%282%29%29%2F%282%29