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Simplifying 4x2 + -29x + 22 = -8 + 2 Reorder the terms: 22 + -29x + 4x2 = -8 + 2 Combine like terms: -8 + 2 = -6 22 + -29x + 4x2 = -6 Solving 22 + -29x + 4x2 = -6 Solving for variable 'x'. Reorder the terms: 22 + 6 + -29x + 4x2 = -6 + 6 Combine like terms: 22 + 6 = 28 28 + -29x + 4x2 = -6 + 6 Combine like terms: -6 + 6 = 0 28 + -29x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 7 + -7.25x + x2 = 0 Move the constant term to the right: Add '-7' to each side of the equation. 7 + -7.25x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + -7.25x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -7.25x + x2 = 0 + -7 -7.25x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 -7.25x + x2 = -7 The x term is -7.25x. Take half its coefficient (-3.625). Square it (13.140625) and add it to both sides. Add '13.140625' to each side of the equation. -7.25x + 13.140625 + x2 = -7 + 13.140625 Reorder the terms: 13.140625 + -7.25x + x2 = -7 + 13.140625 Combine like terms: -7 + 13.140625 = 6.140625 13.140625 + -7.25x + x2 = 6.140625 Factor a perfect square on the left side: (x + -3.625)(x + -3.625) = 6.140625 Calculate the square root of the right side: 2.47802845 Break this problem into two subproblems by setting (x + -3.625) equal to 2.47802845 and -2.47802845.Subproblem 1
x + -3.625 = 2.47802845 Simplifying x + -3.625 = 2.47802845 Reorder the terms: -3.625 + x = 2.47802845 Solving -3.625 + x = 2.47802845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = 2.47802845 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 2.47802845 + 3.625 x = 2.47802845 + 3.625 Combine like terms: 2.47802845 + 3.625 = 6.10302845 x = 6.10302845 Simplifying x = 6.10302845Subproblem 2
x + -3.625 = -2.47802845 Simplifying x + -3.625 = -2.47802845 Reorder the terms: -3.625 + x = -2.47802845 Solving -3.625 + x = -2.47802845 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.625' to each side of the equation. -3.625 + 3.625 + x = -2.47802845 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -2.47802845 + 3.625 x = -2.47802845 + 3.625 Combine like terms: -2.47802845 + 3.625 = 1.14697155 x = 1.14697155 Simplifying x = 1.14697155Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.10302845, 1.14697155}
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