-8x^2+11x+56=0

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Solution for -8x^2+11x+56=0 equation:


Simplifying
-8x2 + 11x + 56 = 0

Reorder the terms:
56 + 11x + -8x2 = 0

Solving
56 + 11x + -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'.
-7 + -1.375x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + -1.375x + 7 + x2 = 0 + 7

Reorder the terms:
-7 + 7 + -1.375x + x2 = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1.375x + x2 = 0 + 7
-1.375x + x2 = 0 + 7

Combine like terms: 0 + 7 = 7
-1.375x + x2 = 7

The x term is -1.375x.  Take half its coefficient (-0.6875).
Square it (0.47265625) and add it to both sides.

Add '0.47265625' to each side of the equation.
-1.375x + 0.47265625 + x2 = 7 + 0.47265625

Reorder the terms:
0.47265625 + -1.375x + x2 = 7 + 0.47265625

Combine like terms: 7 + 0.47265625 = 7.47265625
0.47265625 + -1.375x + x2 = 7.47265625

Factor a perfect square on the left side:
(x + -0.6875)(x + -0.6875) = 7.47265625

Calculate the square root of the right side: 2.733615966

Break this problem into two subproblems by setting 
(x + -0.6875) equal to 2.733615966 and -2.733615966.

Subproblem 1

x + -0.6875 = 2.733615966 Simplifying x + -0.6875 = 2.733615966 Reorder the terms: -0.6875 + x = 2.733615966 Solving -0.6875 + x = 2.733615966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + x = 2.733615966 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = 2.733615966 + 0.6875 x = 2.733615966 + 0.6875 Combine like terms: 2.733615966 + 0.6875 = 3.421115966 x = 3.421115966 Simplifying x = 3.421115966

Subproblem 2

x + -0.6875 = -2.733615966 Simplifying x + -0.6875 = -2.733615966 Reorder the terms: -0.6875 + x = -2.733615966 Solving -0.6875 + x = -2.733615966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6875' to each side of the equation. -0.6875 + 0.6875 + x = -2.733615966 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = -2.733615966 + 0.6875 x = -2.733615966 + 0.6875 Combine like terms: -2.733615966 + 0.6875 = -2.046115966 x = -2.046115966 Simplifying x = -2.046115966

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.421115966, -2.046115966}

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