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Simplifying (-2) * x(4x) + 91 = 33 + -6x Remove parenthesis around (4x) -2x * 4x + 91 = 33 + -6x Reorder the terms for easier multiplication: -2 * 4x * x + 91 = 33 + -6x Multiply -2 * 4 -8x * x + 91 = 33 + -6x Multiply x * x -8x2 + 91 = 33 + -6x Reorder the terms: 91 + -8x2 = 33 + -6x Solving 91 + -8x2 = 33 + -6x Solving for variable 'x'. Reorder the terms: 91 + -33 + 6x + -8x2 = 33 + -6x + -33 + 6x Combine like terms: 91 + -33 = 58 58 + 6x + -8x2 = 33 + -6x + -33 + 6x Reorder the terms: 58 + 6x + -8x2 = 33 + -33 + -6x + 6x Combine like terms: 33 + -33 = 0 58 + 6x + -8x2 = 0 + -6x + 6x 58 + 6x + -8x2 = -6x + 6x Combine like terms: -6x + 6x = 0 58 + 6x + -8x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(29 + 3x + -4x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(29 + 3x + -4x2)' equal to zero and attempt to solve: Simplifying 29 + 3x + -4x2 = 0 Solving 29 + 3x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -7.25 + -0.75x + x2 = 0 Move the constant term to the right: Add '7.25' to each side of the equation. -7.25 + -0.75x + 7.25 + x2 = 0 + 7.25 Reorder the terms: -7.25 + 7.25 + -0.75x + x2 = 0 + 7.25 Combine like terms: -7.25 + 7.25 = 0.00 0.00 + -0.75x + x2 = 0 + 7.25 -0.75x + x2 = 0 + 7.25 Combine like terms: 0 + 7.25 = 7.25 -0.75x + x2 = 7.25 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 = 7.25 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = 7.25 + 0.140625 Combine like terms: 7.25 + 0.140625 = 7.390625 0.140625 + -0.75x + x2 = 7.390625 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = 7.390625 Calculate the square root of the right side: 2.718570396 Break this problem into two subproblems by setting (x + -0.375) equal to 2.718570396 and -2.718570396.Subproblem 1
x + -0.375 = 2.718570396 Simplifying x + -0.375 = 2.718570396 Reorder the terms: -0.375 + x = 2.718570396 Solving -0.375 + x = 2.718570396 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 = 2.718570396 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 2.718570396 + 0.375 x = 2.718570396 + 0.375 Combine like terms: 2.718570396 + 0.375 = 3.093570396 x = 3.093570396 Simplifying x = 3.093570396Subproblem 2
x + -0.375 = -2.718570396 Simplifying x + -0.375 = -2.718570396 Reorder the terms: -0.375 + x = -2.718570396 Solving -0.375 + x = -2.718570396 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 = -2.718570396 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -2.718570396 + 0.375 x = -2.718570396 + 0.375 Combine like terms: -2.718570396 + 0.375 = -2.343570396 x = -2.343570396 Simplifying x = -2.343570396Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.093570396, -2.343570396}Solution
x = {3.093570396, -2.343570396}
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