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Simplifying 30x2 + 3x + -1 = 0 Reorder the terms: -1 + 3x + 30x2 = 0 Solving -1 + 3x + 30x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -0.03333333333 + 0.1x + x2 = 0 Move the constant term to the right: Add '0.03333333333' to each side of the equation. -0.03333333333 + 0.1x + 0.03333333333 + x2 = 0 + 0.03333333333 Reorder the terms: -0.03333333333 + 0.03333333333 + 0.1x + x2 = 0 + 0.03333333333 Combine like terms: -0.03333333333 + 0.03333333333 = 0.00000000000 0.00000000000 + 0.1x + x2 = 0 + 0.03333333333 0.1x + x2 = 0 + 0.03333333333 Combine like terms: 0 + 0.03333333333 = 0.03333333333 0.1x + x2 = 0.03333333333 The x term is 0.1x. Take half its coefficient (0.05). Square it (0.0025) and add it to both sides. Add '0.0025' to each side of the equation. 0.1x + 0.0025 + x2 = 0.03333333333 + 0.0025 Reorder the terms: 0.0025 + 0.1x + x2 = 0.03333333333 + 0.0025 Combine like terms: 0.03333333333 + 0.0025 = 0.03583333333 0.0025 + 0.1x + x2 = 0.03583333333 Factor a perfect square on the left side: (x + 0.05)(x + 0.05) = 0.03583333333 Calculate the square root of the right side: 0.189296945 Break this problem into two subproblems by setting (x + 0.05) equal to 0.189296945 and -0.189296945.Subproblem 1
x + 0.05 = 0.189296945 Simplifying x + 0.05 = 0.189296945 Reorder the terms: 0.05 + x = 0.189296945 Solving 0.05 + x = 0.189296945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = 0.189296945 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = 0.189296945 + -0.05 x = 0.189296945 + -0.05 Combine like terms: 0.189296945 + -0.05 = 0.139296945 x = 0.139296945 Simplifying x = 0.139296945Subproblem 2
x + 0.05 = -0.189296945 Simplifying x + 0.05 = -0.189296945 Reorder the terms: 0.05 + x = -0.189296945 Solving 0.05 + x = -0.189296945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05' to each side of the equation. 0.05 + -0.05 + x = -0.189296945 + -0.05 Combine like terms: 0.05 + -0.05 = 0.00 0.00 + x = -0.189296945 + -0.05 x = -0.189296945 + -0.05 Combine like terms: -0.189296945 + -0.05 = -0.239296945 x = -0.239296945 Simplifying x = -0.239296945Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.139296945, -0.239296945}
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