SOLUTION: Quadratic equation: x^2-12=0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Quadratic equation: x^2-12=0      Log On


   

Question 197254: Quadratic equation: x^2-12=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

x%5E2-12=0 Start with the given equation.


Notice we have a quadratic in the form of Ax%5E2%2BBx%2BC where A=1, B=0, and C=-12


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%28-12%29+%29%29%2F%282%281%29%29 Plug in A=1, B=0, and C=-12


x+=+%280+%2B-+sqrt%28+0-4%281%29%28-12%29+%29%29%2F%282%281%29%29 Square 0 to get 0.


x+=+%280+%2B-+sqrt%28+0--48+%29%29%2F%282%281%29%29 Multiply 4%281%29%28-12%29 to get -48


x+=+%280+%2B-+sqrt%28+0%2B48+%29%29%2F%282%281%29%29 Rewrite sqrt%280--48%29 as sqrt%280%2B48%29


x+=+%280+%2B-+sqrt%28+48+%29%29%2F%282%281%29%29 Add 0 to 48 to get 48


x+=+%280+%2B-+sqrt%28+48+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%280+%2B-+4%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+=+%280%29%2F%282%29+%2B-+%284%2Asqrt%283%29%29%2F%282%29 Break up the fraction.


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


x+=+2%2Asqrt%283%29 or x+=+-2%2Asqrt%283%29 Break up the expression.


So the solutions are x+=+2%2Asqrt%283%29 or x+=+-2%2Asqrt%283%29


which approximate to x=3.464 or x=-3.464