SOLUTION: trying to solve 4x^2+150x=3000

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Question 189563: trying to solve 4x^2+150x=3000
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

4x%5E2%2B150x=3000 Start with the given equation.


4x%5E2%2B150x-3000=0 Subtract 3000 from both sides.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=4, b=150, and c=-3000


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-%28150%29+%2B-+sqrt%28+%28150%29%5E2-4%284%29%28-3000%29+%29%29%2F%282%284%29%29 Plug in a=4, b=150, and c=-3000


x+=+%28-150+%2B-+sqrt%28+22500-4%284%29%28-3000%29+%29%29%2F%282%284%29%29 Square 150 to get 22500.


x+=+%28-150+%2B-+sqrt%28+22500--48000+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-3000%29 to get -48000


x+=+%28-150+%2B-+sqrt%28+22500%2B48000+%29%29%2F%282%284%29%29 Rewrite sqrt%2822500--48000%29 as sqrt%2822500%2B48000%29


x+=+%28-150+%2B-+sqrt%28+70500+%29%29%2F%282%284%29%29 Add 22500 to 48000 to get 70500


x+=+%28-150+%2B-+sqrt%28+70500+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%28-150+%2B-+10%2Asqrt%28705%29%29%2F%288%29 Simplify the square root


x+=+%28-150%2B10%2Asqrt%28705%29%29%2F%288%29 or x+=+%28-150-10%2Asqrt%28705%29%29%2F%288%29 Break up the expression.


x+=+%28-75%2B5%2Asqrt%28705%29%29%2F%284%29 or x+=+%28-75-5%2Asqrt%28705%29%29%2F%284%29 Reduce.


So the answers are x+=+%28-75%2B5%2Asqrt%28705%29%29%2F%284%29 or x+=+%28-75-5%2Asqrt%28705%29%29%2F%284%29


which approximate to x=14.44 or x=-51.94