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Simplifying 4x2 + -3x + -106 = 0 Reorder the terms: -106 + -3x + 4x2 = 0 Solving -106 + -3x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -26.5 + -0.75x + x2 = 0 Move the constant term to the right: Add '26.5' to each side of the equation. -26.5 + -0.75x + 26.5 + x2 = 0 + 26.5 Reorder the terms: -26.5 + 26.5 + -0.75x + x2 = 0 + 26.5 Combine like terms: -26.5 + 26.5 = 0.0 0.0 + -0.75x + x2 = 0 + 26.5 -0.75x + x2 = 0 + 26.5 Combine like terms: 0 + 26.5 = 26.5 -0.75x + x2 = 26.5 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = 26.5 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 26.5 + 0.140625 Combine like terms: 26.5 + 0.140625 = 26.640625 0.140625 + -0.75x + x2 = 26.640625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 26.640625 Calculate the square root of the right side: 5.161455706 Break this problem into two subproblems by setting (x + -0.375) equal to 5.161455706 and -5.161455706.Subproblem 1
x + -0.375 = 5.161455706 Simplifying x + -0.375 = 5.161455706 Reorder the terms: -0.375 + x = 5.161455706 Solving -0.375 + x = 5.161455706 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 5.161455706 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 5.161455706 + 0.375 x = 5.161455706 + 0.375 Combine like terms: 5.161455706 + 0.375 = 5.536455706 x = 5.536455706 Simplifying x = 5.536455706Subproblem 2
x + -0.375 = -5.161455706 Simplifying x + -0.375 = -5.161455706 Reorder the terms: -0.375 + x = -5.161455706 Solving -0.375 + x = -5.161455706 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -5.161455706 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -5.161455706 + 0.375 x = -5.161455706 + 0.375 Combine like terms: -5.161455706 + 0.375 = -4.786455706 x = -4.786455706 Simplifying x = -4.786455706Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.536455706, -4.786455706}
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