SOLUTION: solve: 18x^2+ 9x+2=0 x^2+14x-4=0

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Question 158043: solve:
18x^2+ 9x+2=0
x^2+14x-4=0

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started




18x%5E2%2B9x%2B2=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=18, b=9, and c=2


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-%289%29+%2B-+sqrt%28+%289%29%5E2-4%2818%29%282%29+%29%29%2F%282%2818%29%29 Plug in a=18, b=9, and c=2


x+=+%28-9+%2B-+sqrt%28+81-4%2818%29%282%29+%29%29%2F%282%2818%29%29 Square 9 to get 81.


x+=+%28-9+%2B-+sqrt%28+81-144+%29%29%2F%282%2818%29%29 Multiply 4%2818%29%282%29 to get 144


x+=+%28-9+%2B-+sqrt%28+-63+%29%29%2F%282%2818%29%29 Subtract 144 from 81 to get -63


x+=+%28-9+%2B-+sqrt%28+-63+%29%29%2F%2836%29 Multiply 2 and 18 to get 36.


x+=+%28-9+%2B-+3i%2Asqrt%287%29%29%2F%2836%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-9%2B3i%2Asqrt%287%29%29%2F%2836%29 or x+=+%28-9-3i%2Asqrt%287%29%29%2F%2836%29 Break up the expression.


x+=+%28-3%2Bi%2Asqrt%287%29%29%2F%2812%29 or x+=+%28-3-i%2Asqrt%287%29%29%2F%2812%29 Reduce


So the answers are x+=+%28-3%2Bi%2Asqrt%287%29%29%2F%2812%29 or x+=+%28-3-i%2Asqrt%287%29%29%2F%2812%29


which approximate to x=-0.25%2B0.22%2Ai or x=-0.25-0.22%2Ai