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Simplifying 20x2 + 31x + -12 = 0 Reorder the terms: -12 + 31x + 20x2 = 0 Solving -12 + 31x + 20x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.6 + 1.55x + x2 = 0 Move the constant term to the right: Add '0.6' to each side of the equation. -0.6 + 1.55x + 0.6 + x2 = 0 + 0.6 Reorder the terms: -0.6 + 0.6 + 1.55x + x2 = 0 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + 1.55x + x2 = 0 + 0.6 1.55x + x2 = 0 + 0.6 Combine like terms: 0 + 0.6 = 0.6 1.55x + x2 = 0.6 The x term is 1.55x. Take half its coefficient (0.775). Square it (0.600625) and add it to both sides. Add '0.600625' to each side of the equation. 1.55x + 0.600625 + x2 = 0.6 + 0.600625 Reorder the terms: 0.600625 + 1.55x + x2 = 0.6 + 0.600625 Combine like terms: 0.6 + 0.600625 = 1.200625 0.600625 + 1.55x + x2 = 1.200625 Factor a perfect square on the left side: (x + 0.775)(x + 0.775) = 1.200625 Calculate the square root of the right side: 1.09573035 Break this problem into two subproblems by setting (x + 0.775) equal to 1.09573035 and -1.09573035.Subproblem 1
x + 0.775 = 1.09573035 Simplifying x + 0.775 = 1.09573035 Reorder the terms: 0.775 + x = 1.09573035 Solving 0.775 + x = 1.09573035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.775' to each side of the equation. 0.775 + -0.775 + x = 1.09573035 + -0.775 Combine like terms: 0.775 + -0.775 = 0.000 0.000 + x = 1.09573035 + -0.775 x = 1.09573035 + -0.775 Combine like terms: 1.09573035 + -0.775 = 0.32073035 x = 0.32073035 Simplifying x = 0.32073035Subproblem 2
x + 0.775 = -1.09573035 Simplifying x + 0.775 = -1.09573035 Reorder the terms: 0.775 + x = -1.09573035 Solving 0.775 + x = -1.09573035 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.775' to each side of the equation. 0.775 + -0.775 + x = -1.09573035 + -0.775 Combine like terms: 0.775 + -0.775 = 0.000 0.000 + x = -1.09573035 + -0.775 x = -1.09573035 + -0.775 Combine like terms: -1.09573035 + -0.775 = -1.87073035 x = -1.87073035 Simplifying x = -1.87073035Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.32073035, -1.87073035}
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