SOLUTION: 7x^2-16x-28=0 11x^2=8

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Question 195697: 7x^2-16x-28=0
11x^2=8
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1


7x%5E2-16x-28=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=7, b=-16, and c=-28


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-%28-16%29+%2B-+sqrt%28+%28-16%29%5E2-4%287%29%28-28%29+%29%29%2F%282%287%29%29 Plug in a=7, b=-16, and c=-28


x+=+%2816+%2B-+sqrt%28+%28-16%29%5E2-4%287%29%28-28%29+%29%29%2F%282%287%29%29 Negate -16 to get 16.


x+=+%2816+%2B-+sqrt%28+256-4%287%29%28-28%29+%29%29%2F%282%287%29%29 Square -16 to get 256.


x+=+%2816+%2B-+sqrt%28+256--784+%29%29%2F%282%287%29%29 Multiply 4%287%29%28-28%29 to get -784


x+=+%2816+%2B-+sqrt%28+256%2B784+%29%29%2F%282%287%29%29 Rewrite sqrt%28256--784%29 as sqrt%28256%2B784%29


x+=+%2816+%2B-+sqrt%28+1040+%29%29%2F%282%287%29%29 Add 256 to 784 to get 1040


x+=+%2816+%2B-+sqrt%28+1040+%29%29%2F%2814%29 Multiply 2 and 7 to get 14.


x+=+%2816+%2B-+4%2Asqrt%2865%29%29%2F%2814%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%2816%2B4%2Asqrt%2865%29%29%2F%2814%29 or x+=+%2816-4%2Asqrt%2865%29%29%2F%2814%29 Break up the expression.


x+=+%288%2B2%2Asqrt%2865%29%29%2F%287%29 or x+=+%288-2%2Asqrt%2865%29%29%2F%287%29 Reduce


So the answers are x+=+%288%2B2%2Asqrt%2865%29%29%2F%287%29 or x+=+%288-2%2Asqrt%2865%29%29%2F%287%29


which approximate to x=3.446 or x=-1.161





# 2




11x%5E2=8 Start with the given equation.


x%5E2=8%2F11 Divide both sides by 11.


x=%22%22%2B-sqrt%288%2F11%29 Take the square root of both sides.


x=sqrt%288%2F11%29 or x=-sqrt%288%2F11%29 Break up the "plus/minus" to form two equations.


x=%282%2Asqrt%2822%29%29%2F11 or x=-%282%2Asqrt%2822%29%29%2F11 Simplify the square root.


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Answer:


So the solutions are x=%282%2Asqrt%2822%29%29%2F11 or x=-%282%2Asqrt%2822%29%29%2F11.