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Simplifying 29x2 + 8x + -24 = 0 Reorder the terms: -24 + 8x + 29x2 = 0 Solving -24 + 8x + 29x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 29 the coefficient of the squared term: Divide each side by '29'. -0.8275862069 + 0.275862069x + x2 = 0 Move the constant term to the right: Add '0.8275862069' to each side of the equation. -0.8275862069 + 0.275862069x + 0.8275862069 + x2 = 0 + 0.8275862069 Reorder the terms: -0.8275862069 + 0.8275862069 + 0.275862069x + x2 = 0 + 0.8275862069 Combine like terms: -0.8275862069 + 0.8275862069 = 0.0000000000 0.0000000000 + 0.275862069x + x2 = 0 + 0.8275862069 0.275862069x + x2 = 0 + 0.8275862069 Combine like terms: 0 + 0.8275862069 = 0.8275862069 0.275862069x + x2 = 0.8275862069 The x term is 0.275862069x. Take half its coefficient (0.1379310345). Square it (0.01902497028) and add it to both sides. Add '0.01902497028' to each side of the equation. 0.275862069x + 0.01902497028 + x2 = 0.8275862069 + 0.01902497028 Reorder the terms: 0.01902497028 + 0.275862069x + x2 = 0.8275862069 + 0.01902497028 Combine like terms: 0.8275862069 + 0.01902497028 = 0.84661117718 0.01902497028 + 0.275862069x + x2 = 0.84661117718 Factor a perfect square on the left side: (x + 0.1379310345)(x + 0.1379310345) = 0.84661117718 Calculate the square root of the right side: 0.920114763 Break this problem into two subproblems by setting (x + 0.1379310345) equal to 0.920114763 and -0.920114763.Subproblem 1
x + 0.1379310345 = 0.920114763 Simplifying x + 0.1379310345 = 0.920114763 Reorder the terms: 0.1379310345 + x = 0.920114763 Solving 0.1379310345 + x = 0.920114763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1379310345' to each side of the equation. 0.1379310345 + -0.1379310345 + x = 0.920114763 + -0.1379310345 Combine like terms: 0.1379310345 + -0.1379310345 = 0.0000000000 0.0000000000 + x = 0.920114763 + -0.1379310345 x = 0.920114763 + -0.1379310345 Combine like terms: 0.920114763 + -0.1379310345 = 0.7821837285 x = 0.7821837285 Simplifying x = 0.7821837285Subproblem 2
x + 0.1379310345 = -0.920114763 Simplifying x + 0.1379310345 = -0.920114763 Reorder the terms: 0.1379310345 + x = -0.920114763 Solving 0.1379310345 + x = -0.920114763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1379310345' to each side of the equation. 0.1379310345 + -0.1379310345 + x = -0.920114763 + -0.1379310345 Combine like terms: 0.1379310345 + -0.1379310345 = 0.0000000000 0.0000000000 + x = -0.920114763 + -0.1379310345 x = -0.920114763 + -0.1379310345 Combine like terms: -0.920114763 + -0.1379310345 = -1.0580457975 x = -1.0580457975 Simplifying x = -1.0580457975Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7821837285, -1.0580457975}
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