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Simplifying 0 = 4x2 + -29x + -25 Reorder the terms: 0 = -25 + -29x + 4x2 Solving 0 = -25 + -29x + 4x2 Solving for variable 'x'. Combine like terms: 0 + 25 = 25 25 + 29x + -4x2 = -25 + -29x + 4x2 + 25 + 29x + -4x2 Reorder the terms: 25 + 29x + -4x2 = -25 + 25 + -29x + 29x + 4x2 + -4x2 Combine like terms: -25 + 25 = 0 25 + 29x + -4x2 = 0 + -29x + 29x + 4x2 + -4x2 25 + 29x + -4x2 = -29x + 29x + 4x2 + -4x2 Combine like terms: -29x + 29x = 0 25 + 29x + -4x2 = 0 + 4x2 + -4x2 25 + 29x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 25 + 29x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -6.25 + -7.25x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -7.25x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -7.25x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -7.25x + x2 = 0 + 6.25 -7.25x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -7.25x + x2 = 6.25 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 = 6.25 + 13.140625 Reorder the terms: 13.140625 + -7.25x + x2 = 6.25 + 13.140625 Combine like terms: 6.25 + 13.140625 = 19.390625 13.140625 + -7.25x + x2 = 19.390625 Factor a perfect square on the left side: (x + -3.625)(x + -3.625) = 19.390625 Calculate the square root of the right side: 4.403478738 Break this problem into two subproblems by setting (x + -3.625) equal to 4.403478738 and -4.403478738.Subproblem 1
x + -3.625 = 4.403478738 Simplifying x + -3.625 = 4.403478738 Reorder the terms: -3.625 + x = 4.403478738 Solving -3.625 + x = 4.403478738 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 = 4.403478738 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = 4.403478738 + 3.625 x = 4.403478738 + 3.625 Combine like terms: 4.403478738 + 3.625 = 8.028478738 x = 8.028478738 Simplifying x = 8.028478738Subproblem 2
x + -3.625 = -4.403478738 Simplifying x + -3.625 = -4.403478738 Reorder the terms: -3.625 + x = -4.403478738 Solving -3.625 + x = -4.403478738 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 = -4.403478738 + 3.625 Combine like terms: -3.625 + 3.625 = 0.000 0.000 + x = -4.403478738 + 3.625 x = -4.403478738 + 3.625 Combine like terms: -4.403478738 + 3.625 = -0.778478738 x = -0.778478738 Simplifying x = -0.778478738Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.028478738, -0.778478738}
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