How do I do this Quadratic Equation?

Question

How do I factor this?

x^2+8x-2=0

Answer 1

Can't factor, use other means :

Question Number 1 :

For this equation x^2 + 8*x - 2 = 0 , answer the following questions :

A. Find the roots using Quadratic Formula !

B. Use completing the square to find the root of the equation !

Answer Number 1 :

The equation x^2 + 8*x - 2 = 0 is already in a*x^2+b*x+c=0 form.

In that form, we can easily derive that the value of a = 1, b = 8, c = -2.

1A. Find the roots using Quadratic Formula !

  Remember the formula,

    x1 = (-b+sqrt(b^2-4*a*c))/(2*a) and x2 = (-b-sqrt(b^2-4*a*c))/(2*a)

  As a = 1, b = 8 and c = -2,

  we need to subtitute a,b,c in the abc formula, with thos values.

  So x1 = (-(8) + sqrt( (8)^2 - 4 * (1)*(-2)))/(2*1) and x2 = (-(8) - sqrt( (8)^2 - 4 * (1)*(-2)))/(2*1)

  Which is the same with x1 = ( -8 + sqrt( 64+8))/(2) and x2 = ( -8 - sqrt( 64+8))/(2)

  Which is the same with x1 = ( -8 + sqrt( 72))/(2) and x2 = ( -8 - sqrt( 72))/(2)

  So we get x1 = ( -8 + 8.48528137423857 )/(2) and x2 = ( -8 - 8.48528137423857 )/(2)

  The answers are x1 = 0.242640687119285 and x2 = -8.24264068711928

1B. Use completing the square to find the root of the equation !

  x^2 + 8*x - 2 = 0 ,divide both side with 1

  By doing so we get x^2 + 8*x - 2 = 0 ,

  And the coefficient of x is 8

  We have to use the fact that ( x + q )^2 = x^2 + 2*q*x + q^2 , and assume that q = 8/2 = 4

  Which means we can turn the equation into x^2 + 8*x + 16 - 18 = 0

  And it is the same with ( x + 4 )^2  - 18 = 0

  So we will get (( x + 4 ) - 4.24264068711928 ) * (( x + 4 ) + 4.24264068711928 ) = 0

  And it is the same with ( x + 4 - 4.24264068711928 ) * ( x + 4 + 4.24264068711928 ) = 0

  Just add up the constants in each brackets, and we get ( x - 0.242640687119285 ) * ( x + 8.24264068711928 ) = 0

  So we got the answers as x1 = 0.242640687119285 and x2 = -8.24264068711928

Answer 2

The equation does not factor. However, ou can solve it using the quadrative formula

For ax^2 + bx + c = 0 the solution is

[-b plus or minus sqrt(b*b - 4 * a * c)]/2*a

In this case it is

[-8 plus or minus sqrt(8*8 - 4*(-2)*1)]/2*1

[-8 plus or minus sqrt(64+8)]/2 =

[-8 plus or minus sqrt(72)]/2

sqrt(72) = sqrt(36*2) = sqrt(36)*sqrt(2) = 6*sqrt(2)

[-8 plus or minus 6*sqrt(2)]/2 =

-4 + 3*sqrt(2) and    -4 - 3*sqrt(2)

Answer 3

Use the quadratic formula. x = [-b±√(b²-4ac)]/2a

x = [-8±√56]/2 = -8±2√14/2 = -4±√14