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Simplifying 4x2 + -29x + 45 = -5 + 10 Reorder the terms: 45 + -29x + 4x2 = -5 + 10 Combine like terms: -5 + 10 = 5 45 + -29x + 4x2 = 5 Solving 45 + -29x + 4x2 = 5 Solving for variable 'x'. Reorder the terms: 45 + -5 + -29x + 4x2 = 5 + -5 Combine like terms: 45 + -5 = 40 40 + -29x + 4x2 = 5 + -5 Combine like terms: 5 + -5 = 0 40 + -29x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 10 + -7.25x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -7.25x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -7.25x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -7.25x + x2 = 0 + -10 -7.25x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -7.25x + x2 = -10 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 = -10 + 13.140625 Reorder the terms: 13.140625 + -7.25x + x2 = -10 + 13.140625 Combine like terms: -10 + 13.140625 = 3.140625 13.140625 + -7.25x + x2 = 3.140625 Factor a perfect square on the left side: (x + -3.625)(x + -3.625) = 3.140625 Calculate the square root of the right side: 1.77218086 Break this problem into two subproblems by setting (x + -3.625) equal to 1.77218086 and -1.77218086.Subproblem 1
x + -3.625 = 1.77218086 Simplifying x + -3.625 = 1.77218086 Reorder the terms: -3.625 + x = 1.77218086 Solving -3.625 + x = 1.77218086 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 = 1.77218086 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 1.77218086 + 3.625 x = 1.77218086 + 3.625 Combine like terms: 1.77218086 + 3.625 = 5.39718086 x = 5.39718086 Simplifying x = 5.39718086Subproblem 2
x + -3.625 = -1.77218086 Simplifying x + -3.625 = -1.77218086 Reorder the terms: -3.625 + x = -1.77218086 Solving -3.625 + x = -1.77218086 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 = -1.77218086 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -1.77218086 + 3.625 x = -1.77218086 + 3.625 Combine like terms: -1.77218086 + 3.625 = 1.85281914 x = 1.85281914 Simplifying x = 1.85281914Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.39718086, 1.85281914}
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