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Simplifying 1.44224957x2 + 1.709975947x + -12 = 0 Reorder the terms: -12 + 1.709975947x + 1.44224957x2 = 0 Solving -12 + 1.709975947x + 1.44224957x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.44224957 the coefficient of the squared term: Divide each side by '1.44224957'. -8.320335294 + 1.185631102x + x2 = 0 Move the constant term to the right: Add '8.320335294' to each side of the equation. -8.320335294 + 1.185631102x + 8.320335294 + x2 = 0 + 8.320335294 Reorder the terms: -8.320335294 + 8.320335294 + 1.185631102x + x2 = 0 + 8.320335294 Combine like terms: -8.320335294 + 8.320335294 = 0.000000000 0.000000000 + 1.185631102x + x2 = 0 + 8.320335294 1.185631102x + x2 = 0 + 8.320335294 Combine like terms: 0 + 8.320335294 = 8.320335294 1.185631102x + x2 = 8.320335294 The x term is 1.185631102x. Take half its coefficient (0.592815551). Square it (0.3514302775) and add it to both sides. Add '0.3514302775' to each side of the equation. 1.185631102x + 0.3514302775 + x2 = 8.320335294 + 0.3514302775 Reorder the terms: 0.3514302775 + 1.185631102x + x2 = 8.320335294 + 0.3514302775 Combine like terms: 8.320335294 + 0.3514302775 = 8.6717655715 0.3514302775 + 1.185631102x + x2 = 8.6717655715 Factor a perfect square on the left side: (x + 0.592815551)(x + 0.592815551) = 8.6717655715 Calculate the square root of the right side: 2.944786167 Break this problem into two subproblems by setting (x + 0.592815551) equal to 2.944786167 and -2.944786167.Subproblem 1
x + 0.592815551 = 2.944786167 Simplifying x + 0.592815551 = 2.944786167 Reorder the terms: 0.592815551 + x = 2.944786167 Solving 0.592815551 + x = 2.944786167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.592815551' to each side of the equation. 0.592815551 + -0.592815551 + x = 2.944786167 + -0.592815551 Combine like terms: 0.592815551 + -0.592815551 = 0.000000000 0.000000000 + x = 2.944786167 + -0.592815551 x = 2.944786167 + -0.592815551 Combine like terms: 2.944786167 + -0.592815551 = 2.351970616 x = 2.351970616 Simplifying x = 2.351970616Subproblem 2
x + 0.592815551 = -2.944786167 Simplifying x + 0.592815551 = -2.944786167 Reorder the terms: 0.592815551 + x = -2.944786167 Solving 0.592815551 + x = -2.944786167 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.592815551' to each side of the equation. 0.592815551 + -0.592815551 + x = -2.944786167 + -0.592815551 Combine like terms: 0.592815551 + -0.592815551 = 0.000000000 0.000000000 + x = -2.944786167 + -0.592815551 x = -2.944786167 + -0.592815551 Combine like terms: -2.944786167 + -0.592815551 = -3.537601718 x = -3.537601718 Simplifying x = -3.537601718Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.351970616, -3.537601718}
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