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Simplifying -8x2 + 11x + 5 = 0 Reorder the terms: 5 + 11x + -8x2 = 0 Solving 5 + 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'. -0.625 + -1.375x + x2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -1.375x + 0.625 + x2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -1.375x + x2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -1.375x + x2 = 0 + 0.625 -1.375x + x2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -1.375x + x2 = 0.625 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 = 0.625 + 0.47265625 Reorder the terms: 0.47265625 + -1.375x + x2 = 0.625 + 0.47265625 Combine like terms: 0.625 + 0.47265625 = 1.09765625 0.47265625 + -1.375x + x2 = 1.09765625 Factor a perfect square on the left side: (x + -0.6875)(x + -0.6875) = 1.09765625 Calculate the square root of the right side: 1.047690913 Break this problem into two subproblems by setting (x + -0.6875) equal to 1.047690913 and -1.047690913.Subproblem 1
x + -0.6875 = 1.047690913 Simplifying x + -0.6875 = 1.047690913 Reorder the terms: -0.6875 + x = 1.047690913 Solving -0.6875 + x = 1.047690913 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 = 1.047690913 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = 1.047690913 + 0.6875 x = 1.047690913 + 0.6875 Combine like terms: 1.047690913 + 0.6875 = 1.735190913 x = 1.735190913 Simplifying x = 1.735190913Subproblem 2
x + -0.6875 = -1.047690913 Simplifying x + -0.6875 = -1.047690913 Reorder the terms: -0.6875 + x = -1.047690913 Solving -0.6875 + x = -1.047690913 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 = -1.047690913 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + x = -1.047690913 + 0.6875 x = -1.047690913 + 0.6875 Combine like terms: -1.047690913 + 0.6875 = -0.360190913 x = -0.360190913 Simplifying x = -0.360190913Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.735190913, -0.360190913}
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