8x^2+15x-139=0

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Solution for 8x^2+15x-139=0 equation:


Simplifying
8x2 + 15x + -139 = 0

Reorder the terms:
-139 + 15x + 8x2 = 0

Solving
-139 + 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'.
-17.375 + 1.875x + x2 = 0

Move the constant term to the right:

Add '17.375' to each side of the equation.
-17.375 + 1.875x + 17.375 + x2 = 0 + 17.375

Reorder the terms:
-17.375 + 17.375 + 1.875x + x2 = 0 + 17.375

Combine like terms: -17.375 + 17.375 = 0.000
0.000 + 1.875x + x2 = 0 + 17.375
1.875x + x2 = 0 + 17.375

Combine like terms: 0 + 17.375 = 17.375
1.875x + x2 = 17.375

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 = 17.375 + 0.87890625

Reorder the terms:
0.87890625 + 1.875x + x2 = 17.375 + 0.87890625

Combine like terms: 17.375 + 0.87890625 = 18.25390625
0.87890625 + 1.875x + x2 = 18.25390625

Factor a perfect square on the left side:
(x + 0.9375)(x + 0.9375) = 18.25390625

Calculate the square root of the right side: 4.27245904

Break this problem into two subproblems by setting 
(x + 0.9375) equal to 4.27245904 and -4.27245904.

Subproblem 1

x + 0.9375 = 4.27245904 Simplifying x + 0.9375 = 4.27245904 Reorder the terms: 0.9375 + x = 4.27245904 Solving 0.9375 + x = 4.27245904 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 = 4.27245904 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = 4.27245904 + -0.9375 x = 4.27245904 + -0.9375 Combine like terms: 4.27245904 + -0.9375 = 3.33495904 x = 3.33495904 Simplifying x = 3.33495904

Subproblem 2

x + 0.9375 = -4.27245904 Simplifying x + 0.9375 = -4.27245904 Reorder the terms: 0.9375 + x = -4.27245904 Solving 0.9375 + x = -4.27245904 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 = -4.27245904 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = -4.27245904 + -0.9375 x = -4.27245904 + -0.9375 Combine like terms: -4.27245904 + -0.9375 = -5.20995904 x = -5.20995904 Simplifying x = -5.20995904

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.33495904, -5.20995904}

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