8x^2+3x-6=0

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Solution for 8x^2+3x-6=0 equation:


Simplifying
8x2 + 3x + -6 = 0

Reorder the terms:
-6 + 3x + 8x2 = 0

Solving
-6 + 3x + 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'.
-0.75 + 0.375x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + 0.375x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + 0.375x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + 0.375x + x2 = 0 + 0.75
0.375x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
0.375x + x2 = 0.75

The x term is 0.375x.  Take half its coefficient (0.1875).
Square it (0.03515625) and add it to both sides.

Add '0.03515625' to each side of the equation.
0.375x + 0.03515625 + x2 = 0.75 + 0.03515625

Reorder the terms:
0.03515625 + 0.375x + x2 = 0.75 + 0.03515625

Combine like terms: 0.75 + 0.03515625 = 0.78515625
0.03515625 + 0.375x + x2 = 0.78515625

Factor a perfect square on the left side:
(x + 0.1875)(x + 0.1875) = 0.78515625

Calculate the square root of the right side: 0.88609043

Break this problem into two subproblems by setting 
(x + 0.1875) equal to 0.88609043 and -0.88609043.

Subproblem 1

x + 0.1875 = 0.88609043 Simplifying x + 0.1875 = 0.88609043 Reorder the terms: 0.1875 + x = 0.88609043 Solving 0.1875 + x = 0.88609043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = 0.88609043 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 0.88609043 + -0.1875 x = 0.88609043 + -0.1875 Combine like terms: 0.88609043 + -0.1875 = 0.69859043 x = 0.69859043 Simplifying x = 0.69859043

Subproblem 2

x + 0.1875 = -0.88609043 Simplifying x + 0.1875 = -0.88609043 Reorder the terms: 0.1875 + x = -0.88609043 Solving 0.1875 + x = -0.88609043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1875' to each side of the equation. 0.1875 + -0.1875 + x = -0.88609043 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -0.88609043 + -0.1875 x = -0.88609043 + -0.1875 Combine like terms: -0.88609043 + -0.1875 = -1.07359043 x = -1.07359043 Simplifying x = -1.07359043

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.69859043, -1.07359043}

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