Questions on Algebra: Quadratic Equation answered by real tutors!

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Question 151430: x^2-4x+8=0 .
4x^2-6x-1=0 .
x^2+x+2=0 .

3x^2-x-1=0 .: x^2-4x+8=0 .
4x^2-6x-1=0 .
x^2+x+2=0 .

3x^2-x-1=0 .
Answer by jim_thompson5910(9421) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you started.


# 1


x^2-4x+8=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax^2+bx+c where a=1, b=-4, and c=8


Let's use the quadratic formula to solve for x


x = (-b +- sqrt( b^2-4ac ))/(2a) Start with the quadratic formula


x = (-(-4) +- sqrt( (-4)^2-4(1)(8) ))/(2(1)) Plug in a=1, b=-4, and c=8


x = (4 +- sqrt( (-4)^2-4(1)(8) ))/(2(1)) Negate -4 to get 4.


x = (4 +- sqrt( 16-4(1)(8) ))/(2(1)) Square -4 to get 16.


x = (4 +- sqrt( 16-32 ))/(2(1)) Multiply 4(1)(8) to get 32


x = (4 +- sqrt( -16 ))/(2(1)) Subtract 32 from 16 to get -16


x = (4 +- sqrt( -16 ))/(2) Multiply 2 and 1 to get 2.


x = (4 +- 4*i)/(2) Take the square root of -16 to get 4*i.


x = (4 + 4*i)/(2) or x = (4 - 4*i)/(2) Break up the expression.


x = (4)/(2) + (4*i)/(2) or x = (4)/(2) - (4*i)/(2) Break up the fraction for each case.


x = 2+2*i or x = 2-2*i Reduce.


x = 2+2*i or x = 2-2*i Simplify.


So our answers are x = 2+2*i or x = 2-2*i





# 2


4x^2-6x-1=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax^2+bx+c where a=4, b=-6, and c=-1


Let's use the quadratic formula to solve for x


x = (-b +- sqrt( b^2-4ac ))/(2a) Start with the quadratic formula


x = (-(-6) +- sqrt( (-6)^2-4(4)(-1) ))/(2(4)) Plug in a=4, b=-6, and c=-1


x = (6 +- sqrt( (-6)^2-4(4)(-1) ))/(2(4)) Negate -6 to get 6.


x = (6 +- sqrt( 36-4(4)(-1) ))/(2(4)) Square -6 to get 36.


x = (6 +- sqrt( 36--16 ))/(2(4)) Multiply 4(4)(-1) to get -16


x = (6 +- sqrt( 36+16 ))/(2(4)) Rewrite sqrt(36--16) as sqrt(36+16)


x = (6 +- sqrt( 52 ))/(2(4)) Add 36 to 16 to get 52


x = (6 +- sqrt( 52 ))/(8) Multiply 2 and 4 to get 8.


x = (6 +- 2*sqrt(13))/(8) Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x = (6+2*sqrt(13))/(8) or x = (6-2*sqrt(13))/(8) Break up the expression.


x = (3+sqrt(13))/(4) or x = (4-sqrt(13))/(4) Reduce.


So the answers are x = (3+sqrt(13))/(4) or x = (4-sqrt(13))/(4)


which approximate to x=1.651 or x=-0.151