SOLUTION: Please help solve the following equation: 600 = 0.9x^ - 26.5x + 290 Thanks.

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Question 188334: Please help solve the following equation:
600 = 0.9x^ - 26.5x + 290
Thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'm assuming that the equation should be 600+=+0.9x%5E2+-+26.5x+%2B+290



600+=+0.9x%5E2+-+26.5x+%2B+290 Start with the given equation.


6000+=+9x%5E2+-+265x+%2B+2900 Multiply EVERY term by 10 to make every number a whole number


0+=+9x%5E2+-+265x+%2B+2900-6000 Subtract 6000 from both sides.


0+=+9x%5E2+-+265x+-3100 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=9, b=-265, and c=-3100


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-%28-265%29+%2B-+sqrt%28+%28-265%29%5E2-4%289%29%28-3100%29+%29%29%2F%282%289%29%29 Plug in a=9, b=-265, and c=-3100


x+=+%28265+%2B-+sqrt%28+%28-265%29%5E2-4%289%29%28-3100%29+%29%29%2F%282%289%29%29 Negate -265 to get 265.


x+=+%28265+%2B-+sqrt%28+70225-4%289%29%28-3100%29+%29%29%2F%282%289%29%29 Square -265 to get 70225.


x+=+%28265+%2B-+sqrt%28+70225--111600+%29%29%2F%282%289%29%29 Multiply 4%289%29%28-3100%29 to get -111600


x+=+%28265+%2B-+sqrt%28+70225%2B111600+%29%29%2F%282%289%29%29 Rewrite sqrt%2870225--111600%29 as sqrt%2870225%2B111600%29


x+=+%28265+%2B-+sqrt%28+181825+%29%29%2F%282%289%29%29 Add 70225 to 111600 to get 181825


x+=+%28265+%2B-+sqrt%28+181825+%29%29%2F%2818%29 Multiply 2 and 9 to get 18.


x+=+%28265+%2B-+5%2Asqrt%287273%29%29%2F%2818%29 Simplify the square root


x+=+%28265%2B5%2Asqrt%287273%29%29%2F%2818%29 or x+=+%28265-5%2Asqrt%287273%29%29%2F%2818%29 Break up the expression.


So the answers are x+=+%28265%2B5%2Asqrt%287273%29%29%2F%2818%29 or x+=+%28265-5%2Asqrt%287273%29%29%2F%2818%29


which approximate to x=38.412 or x=-8.967