5x^2-4x-8=0

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Solution for 5x^2-4x-8=0 equation:


Simplifying
5x2 + -4x + -8 = 0

Reorder the terms:
-8 + -4x + 5x2 = 0

Solving
-8 + -4x + 5x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
5 the coefficient of the squared term: 

Divide each side by '5'.
-1.6 + -0.8x + x2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + -0.8x + 1.6 + x2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + -0.8x + x2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + -0.8x + x2 = 0 + 1.6
-0.8x + x2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
-0.8x + x2 = 1.6

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = 1.6 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = 1.6 + 0.16

Combine like terms: 1.6 + 0.16 = 1.76
0.16 + -0.8x + x2 = 1.76

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = 1.76

Calculate the square root of the right side: 1.326649916

Break this problem into two subproblems by setting 
(x + -0.4) equal to 1.326649916 and -1.326649916.

Subproblem 1

x + -0.4 = 1.326649916 Simplifying x + -0.4 = 1.326649916 Reorder the terms: -0.4 + x = 1.326649916 Solving -0.4 + x = 1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = 1.326649916 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = 1.326649916 + 0.4 x = 1.326649916 + 0.4 Combine like terms: 1.326649916 + 0.4 = 1.726649916 x = 1.726649916 Simplifying x = 1.726649916

Subproblem 2

x + -0.4 = -1.326649916 Simplifying x + -0.4 = -1.326649916 Reorder the terms: -0.4 + x = -1.326649916 Solving -0.4 + x = -1.326649916 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4' to each side of the equation. -0.4 + 0.4 + x = -1.326649916 + 0.4 Combine like terms: -0.4 + 0.4 = 0.0 0.0 + x = -1.326649916 + 0.4 x = -1.326649916 + 0.4 Combine like terms: -1.326649916 + 0.4 = -0.926649916 x = -0.926649916 Simplifying x = -0.926649916

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.726649916, -0.926649916}

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