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Simplifying 2x2 + -23x + -29 = 0 Reorder the terms: -29 + -23x + 2x2 = 0 Solving -29 + -23x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -14.5 + -11.5x + x2 = 0 Move the constant term to the right: Add '14.5' to each side of the equation. -14.5 + -11.5x + 14.5 + x2 = 0 + 14.5 Reorder the terms: -14.5 + 14.5 + -11.5x + x2 = 0 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + -11.5x + x2 = 0 + 14.5 -11.5x + x2 = 0 + 14.5 Combine like terms: 0 + 14.5 = 14.5 -11.5x + x2 = 14.5 The x term is -11.5x. Take half its coefficient (-5.75). Square it (33.0625) and add it to both sides. Add '33.0625' to each side of the equation. -11.5x + 33.0625 + x2 = 14.5 + 33.0625 Reorder the terms: 33.0625 + -11.5x + x2 = 14.5 + 33.0625 Combine like terms: 14.5 + 33.0625 = 47.5625 33.0625 + -11.5x + x2 = 47.5625 Factor a perfect square on the left side: (x + -5.75)(x + -5.75) = 47.5625 Calculate the square root of the right side: 6.896557112 Break this problem into two subproblems by setting (x + -5.75) equal to 6.896557112 and -6.896557112.Subproblem 1
x + -5.75 = 6.896557112 Simplifying x + -5.75 = 6.896557112 Reorder the terms: -5.75 + x = 6.896557112 Solving -5.75 + x = 6.896557112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = 6.896557112 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = 6.896557112 + 5.75 x = 6.896557112 + 5.75 Combine like terms: 6.896557112 + 5.75 = 12.646557112 x = 12.646557112 Simplifying x = 12.646557112Subproblem 2
x + -5.75 = -6.896557112 Simplifying x + -5.75 = -6.896557112 Reorder the terms: -5.75 + x = -6.896557112 Solving -5.75 + x = -6.896557112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.75' to each side of the equation. -5.75 + 5.75 + x = -6.896557112 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + x = -6.896557112 + 5.75 x = -6.896557112 + 5.75 Combine like terms: -6.896557112 + 5.75 = -1.146557112 x = -1.146557112 Simplifying x = -1.146557112Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.646557112, -1.146557112}
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