SOLUTION: quadratic formula: solve the equation 2x^2+12x-6=0 x^2-6x+7=0 3x^2+11x+10=0 please solve them i really need helppp soonnnn

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: quadratic formula: solve the equation 2x^2+12x-6=0 x^2-6x+7=0 3x^2+11x+10=0 please solve them i really need helppp soonnnn       Log On


   

Question 448632: quadratic formula: solve the equation
2x^2+12x-6=0

x^2-6x+7=0
3x^2+11x+10=0
please solve them i really need helppp soonnnn
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you started.

# 1

2x%5E2%2B12x-6=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=2, b=12, and c=-6


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-%2812%29+%2B-+sqrt%28+%2812%29%5E2-4%282%29%28-6%29+%29%29%2F%282%282%29%29 Plug in a=2, b=12, and c=-6


x+=+%28-12+%2B-+sqrt%28+144-4%282%29%28-6%29+%29%29%2F%282%282%29%29 Square 12 to get 144.


x+=+%28-12+%2B-+sqrt%28+144--48+%29%29%2F%282%282%29%29 Multiply 4%282%29%28-6%29 to get -48


x+=+%28-12+%2B-+sqrt%28+144%2B48+%29%29%2F%282%282%29%29 Rewrite sqrt%28144--48%29 as sqrt%28144%2B48%29


x+=+%28-12+%2B-+sqrt%28+192+%29%29%2F%282%282%29%29 Add 144 to 48 to get 192


x+=+%28-12+%2B-+sqrt%28+192+%29%29%2F%284%29 Multiply 2 and 2 to get 4.


x+=+%28-12+%2B-+8%2Asqrt%283%29%29%2F%284%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-12%29%2F%284%29+%2B-+%288%2Asqrt%283%29%29%2F%284%29 Break up the fraction.


x+=+-3+%2B-+2%2Asqrt%283%29 Reduce.


x+=+-3%2B2%2Asqrt%283%29 or x+=+-3-2%2Asqrt%283%29 Break up the expression.


So the answers are x+=+-3%2B2%2Asqrt%283%29 or x+=+-3-2%2Asqrt%283%29

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# 2
x%5E2-6x%2B7=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-6, and c=7


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-%28-6%29+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%287%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-6, and c=7


x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%281%29%287%29+%29%29%2F%282%281%29%29 Negate -6 to get 6.


x+=+%286+%2B-+sqrt%28+36-4%281%29%287%29+%29%29%2F%282%281%29%29 Square -6 to get 36.


x+=+%286+%2B-+sqrt%28+36-28+%29%29%2F%282%281%29%29 Multiply 4%281%29%287%29 to get 28


x+=+%286+%2B-+sqrt%28+8+%29%29%2F%282%281%29%29 Subtract 28 from 36 to get 8


x+=+%286+%2B-+sqrt%28+8+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%286+%2B-+2%2Asqrt%282%29%29%2F%282%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%286%29%2F%282%29+%2B-+%282%2Asqrt%282%29%29%2F%282%29 Break up the fraction.


x+=+3+%2B-+sqrt%282%29 Reduce.


x+=+3%2Bsqrt%282%29 or x+=+3-sqrt%282%29 Break up the expression.


So the answers are x+=+3%2Bsqrt%282%29 or x+=+3-sqrt%282%29