8x^2-5x-4=0

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


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

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

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

Solving for variable 'x'.

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

Divide each side by '8'.
-0.5 + -0.625x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -0.625x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -0.625x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -0.625x + x2 = 0 + 0.5
-0.625x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-0.625x + x2 = 0.5

The x term is -0.625x.  Take half its coefficient (-0.3125).
Square it (0.09765625) and add it to both sides.

Add '0.09765625' to each side of the equation.
-0.625x + 0.09765625 + x2 = 0.5 + 0.09765625

Reorder the terms:
0.09765625 + -0.625x + x2 = 0.5 + 0.09765625

Combine like terms: 0.5 + 0.09765625 = 0.59765625
0.09765625 + -0.625x + x2 = 0.59765625

Factor a perfect square on the left side:
(x + -0.3125)(x + -0.3125) = 0.59765625

Calculate the square root of the right side: 0.773082305

Break this problem into two subproblems by setting 
(x + -0.3125) equal to 0.773082305 and -0.773082305.

Subproblem 1

x + -0.3125 = 0.773082305 Simplifying x + -0.3125 = 0.773082305 Reorder the terms: -0.3125 + x = 0.773082305 Solving -0.3125 + x = 0.773082305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 0.773082305 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 0.773082305 + 0.3125 x = 0.773082305 + 0.3125 Combine like terms: 0.773082305 + 0.3125 = 1.085582305 x = 1.085582305 Simplifying x = 1.085582305

Subproblem 2

x + -0.3125 = -0.773082305 Simplifying x + -0.3125 = -0.773082305 Reorder the terms: -0.3125 + x = -0.773082305 Solving -0.3125 + x = -0.773082305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -0.773082305 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -0.773082305 + 0.3125 x = -0.773082305 + 0.3125 Combine like terms: -0.773082305 + 0.3125 = -0.460582305 x = -0.460582305 Simplifying x = -0.460582305

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.085582305, -0.460582305}

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