8x^2-15x-8=0

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Solution for 8x^2-15x-8=0 equation:


Simplifying
8x2 + -15x + -8 = 0

Reorder the terms:
-8 + -15x + 8x2 = 0

Solving
-8 + -15x + 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'.
-1 + -1.875x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -1.875x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -1.875x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1.875x + x2 = 0 + 1
-1.875x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1.875x + x2 = 1

The x term is -1.875x.  Take half its coefficient (-0.9375).
Square it (0.87890625) and add it to both sides.

Add '0.87890625' to each side of the equation.
-1.875x + 0.87890625 + x2 = 1 + 0.87890625

Reorder the terms:
0.87890625 + -1.875x + x2 = 1 + 0.87890625

Combine like terms: 1 + 0.87890625 = 1.87890625
0.87890625 + -1.875x + x2 = 1.87890625

Factor a perfect square on the left side:
(x + -0.9375)(x + -0.9375) = 1.87890625

Calculate the square root of the right side: 1.370732012

Break this problem into two subproblems by setting 
(x + -0.9375) equal to 1.370732012 and -1.370732012.

Subproblem 1

x + -0.9375 = 1.370732012 Simplifying x + -0.9375 = 1.370732012 Reorder the terms: -0.9375 + x = 1.370732012 Solving -0.9375 + x = 1.370732012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = 1.370732012 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = 1.370732012 + 0.9375 x = 1.370732012 + 0.9375 Combine like terms: 1.370732012 + 0.9375 = 2.308232012 x = 2.308232012 Simplifying x = 2.308232012

Subproblem 2

x + -0.9375 = -1.370732012 Simplifying x + -0.9375 = -1.370732012 Reorder the terms: -0.9375 + x = -1.370732012 Solving -0.9375 + x = -1.370732012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9375' to each side of the equation. -0.9375 + 0.9375 + x = -1.370732012 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + x = -1.370732012 + 0.9375 x = -1.370732012 + 0.9375 Combine like terms: -1.370732012 + 0.9375 = -0.433232012 x = -0.433232012 Simplifying x = -0.433232012

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.308232012, -0.433232012}

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