SOLUTION: 7x^2+58x=16

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Question 101320: 7x^2+58x=16
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
7x%5E2%2B58x=16 Start with the given equation


7x%5E2%2B58x-16=0 Subtract 16 from both sides


Solved by pluggable solver: Quadratic Formula
Let's use the quadratic formula to solve for x:


Starting with the general quadratic


ax%5E2%2Bbx%2Bc=0


the general solution using the quadratic equation is:


x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29




So lets solve 7%2Ax%5E2%2B58%2Ax-16=0 ( notice a=7, b=58, and c=-16)





x+=+%28-58+%2B-+sqrt%28+%2858%29%5E2-4%2A7%2A-16+%29%29%2F%282%2A7%29 Plug in a=7, b=58, and c=-16




x+=+%28-58+%2B-+sqrt%28+3364-4%2A7%2A-16+%29%29%2F%282%2A7%29 Square 58 to get 3364




x+=+%28-58+%2B-+sqrt%28+3364%2B448+%29%29%2F%282%2A7%29 Multiply -4%2A-16%2A7 to get 448




x+=+%28-58+%2B-+sqrt%28+3812+%29%29%2F%282%2A7%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-58+%2B-+2%2Asqrt%28953%29%29%2F%282%2A7%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)




x+=+%28-58+%2B-+2%2Asqrt%28953%29%29%2F14 Multiply 2 and 7 to get 14


So now the expression breaks down into two parts


x+=+%28-58+%2B+2%2Asqrt%28953%29%29%2F14 or x+=+%28-58+-+2%2Asqrt%28953%29%29%2F14



Now break up the fraction



x=-58%2F14%2B2%2Asqrt%28953%29%2F14 or x=-58%2F14-2%2Asqrt%28953%29%2F14



Simplify



x=-29%2F7%2Bsqrt%28953%29%2F7 or x=-29%2F7-sqrt%28953%29%2F7



So the solutions are:

x=-29%2F7%2Bsqrt%28953%29%2F7 or x=-29%2F7-sqrt%28953%29%2F7