SOLUTION: Solve. e^(4x^2+12x+9)= 1

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Question 202846: Solve. e^(4x^2+12x+9)= 1
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
e%5E%284x%5E2%2B12x%2B9%29=1 Start with the given equation.


ln%28e%5E%284x%5E2%2B12x%2B9%29%29=ln%281%29 Take the natural log of both sides


4x%5E2%2B12x%2B9=ln%281%29 Evaluate the natural log of e%5E%284x%5E2%2B12x%2B9%29 to get 4x%5E2%2B12x%2B9


4x%5E2%2B12x%2B9=0 Evaluate the natural log of 1 to get 0


Notice that the quadratic 4x%5E2%2B12x%2B9 is in the form of Ax%5E2%2BBx%2BC where A=4, B=12, 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-%2812%29+%2B-+sqrt%28+%2812%29%5E2-4%284%29%289%29+%29%29%2F%282%284%29%29 Plug in A=4, B=12, and C=9


x+=+%28-12+%2B-+sqrt%28+144-4%284%29%289%29+%29%29%2F%282%284%29%29 Square 12 to get 144.


x+=+%28-12+%2B-+sqrt%28+144-144+%29%29%2F%282%284%29%29 Multiply 4%284%29%289%29 to get 144


x+=+%28-12+%2B-+sqrt%28+0+%29%29%2F%282%284%29%29 Subtract 144 from 144 to get 0


x+=+%28-12+%2B-+sqrt%28+0+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%28-12+%2B-+0%29%2F%288%29 Take the square root of 0 to get 0.


x+=+%28-12+%2B+0%29%2F%288%29 or x+=+%28-12+-+0%29%2F%288%29 Break up the expression.


x+=+%28-12%29%2F%288%29 or x+=++%28-12%29%2F%288%29 Combine like terms.


x+=+-3%2F2 or x+=+-3%2F2 Simplify.


So the only solution is x+=+-3%2F2