SOLUTION: Will the quadratic equation work on an equation such as x^2 - 3=0?

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Question 151432: Will the quadratic equation work on an equation such as x^2 - 3=0?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-3=0 Start with the given equation.


Take note that x%5E2-3=0 really looks like x%5E2%2B0x%2B%28-3%29=0


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=0, and c=-3


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-%280%29+%2B-+sqrt%28+%280%29%5E2-4%281%29%28-3%29+%29%29%2F%282%281%29%29 Plug in a=1, b=0, and c=-3


x+=+%28-0+%2B-+sqrt%28+0-4%281%29%28-3%29+%29%29%2F%282%281%29%29 Square 0 to get 0.


x+=+%28-0+%2B-+sqrt%28+0--12+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-3%29 to get -12


x+=+%28-0+%2B-+sqrt%28+0%2B12+%29%29%2F%282%281%29%29 Rewrite sqrt%280--12%29 as sqrt%280%2B12%29


x+=+%28-0+%2B-+sqrt%28+12+%29%29%2F%282%281%29%29 Add 0 to 12 to get 12


x+=+%28-0+%2B-+sqrt%28+12+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%28-0+%2B-+2%2Asqrt%283%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-0%29%2F%282%29+%2B-+%282%2Asqrt%283%29%29%2F%282%29 Break up the fraction.


x+=+0+%2B-+sqrt%283%29 Reduce.


x+=+sqrt%283%29 or x+=+-sqrt%283%29 Break up the expression.


So our answers are x+=+sqrt%283%29 or x+=+-sqrt%283%29


which approximate to x=1.732 or x=-1.732


Note: even though the quadratic formula works perfectly here, there is a much faster way to solve this problem.