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

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: {{{ x^2-4x+8=0 }}}. {{{ 4x^2-6x-1=0 }}}. {{{ x^2+x+2=0 }}}. {{{ 3x^2-x-1=0 }}}.      Log On


   

Question 151430: +x%5E2-4x%2B8=0+.
+4x%5E2-6x-1=0+.
+x%5E2%2Bx%2B2=0+.

+3x%5E2-x-1=0+.
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


x%5E2-4x%2B8=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=1, b=-4, and c=8


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-%28-4%29+%2B-+sqrt%28+%28-4%29%5E2-4%281%29%288%29+%29%29%2F%282%281%29%29 Plug in a=1, b=-4, and c=8


x+=+%284+%2B-+sqrt%28+%28-4%29%5E2-4%281%29%288%29+%29%29%2F%282%281%29%29 Negate -4 to get 4.


x+=+%284+%2B-+sqrt%28+16-4%281%29%288%29+%29%29%2F%282%281%29%29 Square -4 to get 16.


x+=+%284+%2B-+sqrt%28+16-32+%29%29%2F%282%281%29%29 Multiply 4%281%29%288%29 to get 32


x+=+%284+%2B-+sqrt%28+-16+%29%29%2F%282%281%29%29 Subtract 32 from 16 to get -16


x+=+%284+%2B-+sqrt%28+-16+%29%29%2F%282%29 Multiply 2 and 1 to get 2.


x+=+%284+%2B-+4%2Ai%29%2F%282%29 Take the square root of -16 to get 4%2Ai.


x+=+%284+%2B+4%2Ai%29%2F%282%29 or x+=+%284+-+4%2Ai%29%2F%282%29 Break up the expression.


x+=+%284%29%2F%282%29+%2B+%284%2Ai%29%2F%282%29 or x+=++%284%29%2F%282%29+-+%284%2Ai%29%2F%282%29 Break up the fraction for each case.


x+=+2%2B2%2Ai or x+=++2-2%2Ai Reduce.


x+=+2%2B2%2Ai or x+=+2-2%2Ai Simplify.


So our answers are x+=+2%2B2%2Ai or x+=+2-2%2Ai





# 2


4x%5E2-6x-1=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=4, b=-6, and c=-1


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%284%29%28-1%29+%29%29%2F%282%284%29%29 Plug in a=4, b=-6, and c=-1


x+=+%286+%2B-+sqrt%28+%28-6%29%5E2-4%284%29%28-1%29+%29%29%2F%282%284%29%29 Negate -6 to get 6.


x+=+%286+%2B-+sqrt%28+36-4%284%29%28-1%29+%29%29%2F%282%284%29%29 Square -6 to get 36.


x+=+%286+%2B-+sqrt%28+36--16+%29%29%2F%282%284%29%29 Multiply 4%284%29%28-1%29 to get -16


x+=+%286+%2B-+sqrt%28+36%2B16+%29%29%2F%282%284%29%29 Rewrite sqrt%2836--16%29 as sqrt%2836%2B16%29


x+=+%286+%2B-+sqrt%28+52+%29%29%2F%282%284%29%29 Add 36 to 16 to get 52


x+=+%286+%2B-+sqrt%28+52+%29%29%2F%288%29 Multiply 2 and 4 to get 8.


x+=+%286+%2B-+2%2Asqrt%2813%29%29%2F%288%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%286%2B2%2Asqrt%2813%29%29%2F%288%29 or x+=+%286-2%2Asqrt%2813%29%29%2F%288%29 Break up the expression.


x+=+%283%2Bsqrt%2813%29%29%2F%284%29 or x+=+%284-sqrt%2813%29%29%2F%284%29 Reduce.


So the answers are x+=+%283%2Bsqrt%2813%29%29%2F%284%29 or x+=+%284-sqrt%2813%29%29%2F%284%29


which approximate to x=1.651 or x=-0.151