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Simplifying 10x2 + -29x + -25 = 0 Reorder the terms: -25 + -29x + 10x2 = 0 Solving -25 + -29x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.5 + -2.9x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -2.9x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -2.9x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -2.9x + x2 = 0 + 2.5 -2.9x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -2.9x + x2 = 2.5 The x term is -2.9x. Take half its coefficient (-1.45). Square it (2.1025) and add it to both sides. Add '2.1025' to each side of the equation. -2.9x + 2.1025 + x2 = 2.5 + 2.1025 Reorder the terms: 2.1025 + -2.9x + x2 = 2.5 + 2.1025 Combine like terms: 2.5 + 2.1025 = 4.6025 2.1025 + -2.9x + x2 = 4.6025 Factor a perfect square on the left side: (x + -1.45)(x + -1.45) = 4.6025 Calculate the square root of the right side: 2.145343795 Break this problem into two subproblems by setting (x + -1.45) equal to 2.145343795 and -2.145343795.Subproblem 1
x + -1.45 = 2.145343795 Simplifying x + -1.45 = 2.145343795 Reorder the terms: -1.45 + x = 2.145343795 Solving -1.45 + x = 2.145343795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.45' to each side of the equation. -1.45 + 1.45 + x = 2.145343795 + 1.45 Combine like terms: -1.45 + 1.45 = 0.00 0.00 + x = 2.145343795 + 1.45 x = 2.145343795 + 1.45 Combine like terms: 2.145343795 + 1.45 = 3.595343795 x = 3.595343795 Simplifying x = 3.595343795Subproblem 2
x + -1.45 = -2.145343795 Simplifying x + -1.45 = -2.145343795 Reorder the terms: -1.45 + x = -2.145343795 Solving -1.45 + x = -2.145343795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.45' to each side of the equation. -1.45 + 1.45 + x = -2.145343795 + 1.45 Combine like terms: -1.45 + 1.45 = 0.00 0.00 + x = -2.145343795 + 1.45 x = -2.145343795 + 1.45 Combine like terms: -2.145343795 + 1.45 = -0.695343795 x = -0.695343795 Simplifying x = -0.695343795Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.595343795, -0.695343795}
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