8x^2+3x-8=0

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


Simplifying
8x2 + 3x + -8 = 0

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

Solving
-8 + 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'.
-1 + 0.375x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 0.375x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 0.375x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 0.375x + x2 = 0 + 1
0.375x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
0.375x + x2 = 1

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 = 1 + 0.03515625

Reorder the terms:
0.03515625 + 0.375x + x2 = 1 + 0.03515625

Combine like terms: 1 + 0.03515625 = 1.03515625
0.03515625 + 0.375x + x2 = 1.03515625

Factor a perfect square on the left side:
(x + 0.1875)(x + 0.1875) = 1.03515625

Calculate the square root of the right side: 1.017426287

Break this problem into two subproblems by setting 
(x + 0.1875) equal to 1.017426287 and -1.017426287.

Subproblem 1

x + 0.1875 = 1.017426287 Simplifying x + 0.1875 = 1.017426287 Reorder the terms: 0.1875 + x = 1.017426287 Solving 0.1875 + x = 1.017426287 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 = 1.017426287 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = 1.017426287 + -0.1875 x = 1.017426287 + -0.1875 Combine like terms: 1.017426287 + -0.1875 = 0.829926287 x = 0.829926287 Simplifying x = 0.829926287

Subproblem 2

x + 0.1875 = -1.017426287 Simplifying x + 0.1875 = -1.017426287 Reorder the terms: 0.1875 + x = -1.017426287 Solving 0.1875 + x = -1.017426287 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 = -1.017426287 + -0.1875 Combine like terms: 0.1875 + -0.1875 = 0.0000 0.0000 + x = -1.017426287 + -0.1875 x = -1.017426287 + -0.1875 Combine like terms: -1.017426287 + -0.1875 = -1.204926287 x = -1.204926287 Simplifying x = -1.204926287

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.829926287, -1.204926287}

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