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Simplifying 4x2 + -29x + 13 = 0 Reorder the terms: 13 + -29x + 4x2 = 0 Solving 13 + -29x + 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'. 3.25 + -7.25x + x2 = 0 Move the constant term to the right: Add '-3.25' to each side of the equation. 3.25 + -7.25x + -3.25 + x2 = 0 + -3.25 Reorder the terms: 3.25 + -3.25 + -7.25x + x2 = 0 + -3.25 Combine like terms: 3.25 + -3.25 = 0.00 0.00 + -7.25x + x2 = 0 + -3.25 -7.25x + x2 = 0 + -3.25 Combine like terms: 0 + -3.25 = -3.25 -7.25x + x2 = -3.25 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 = -3.25 + 13.140625 Reorder the terms: 13.140625 + -7.25x + x2 = -3.25 + 13.140625 Combine like terms: -3.25 + 13.140625 = 9.890625 13.140625 + -7.25x + x2 = 9.890625 Factor a perfect square on the left side: (x + -3.625)(x + -3.625) = 9.890625 Calculate the square root of the right side: 3.144936406 Break this problem into two subproblems by setting (x + -3.625) equal to 3.144936406 and -3.144936406.Subproblem 1
x + -3.625 = 3.144936406 Simplifying x + -3.625 = 3.144936406 Reorder the terms: -3.625 + x = 3.144936406 Solving -3.625 + x = 3.144936406 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 = 3.144936406 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 3.144936406 + 3.625 x = 3.144936406 + 3.625 Combine like terms: 3.144936406 + 3.625 = 6.769936406 x = 6.769936406 Simplifying x = 6.769936406Subproblem 2
x + -3.625 = -3.144936406 Simplifying x + -3.625 = -3.144936406 Reorder the terms: -3.625 + x = -3.144936406 Solving -3.625 + x = -3.144936406 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 = -3.144936406 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -3.144936406 + 3.625 x = -3.144936406 + 3.625 Combine like terms: -3.144936406 + 3.625 = 0.480063594 x = 0.480063594 Simplifying x = 0.480063594Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.769936406, 0.480063594}
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