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Simplifying 30x2 + -31x + 3 = 0 Reorder the terms: 3 + -31x + 30x2 = 0 Solving 3 + -31x + 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'. 0.1 + -1.033333333x + x2 = 0 Move the constant term to the right: Add '-0.1' to each side of the equation. 0.1 + -1.033333333x + -0.1 + x2 = 0 + -0.1 Reorder the terms: 0.1 + -0.1 + -1.033333333x + x2 = 0 + -0.1 Combine like terms: 0.1 + -0.1 = 0.0 0.0 + -1.033333333x + x2 = 0 + -0.1 -1.033333333x + x2 = 0 + -0.1 Combine like terms: 0 + -0.1 = -0.1 -1.033333333x + x2 = -0.1 The x term is -1.033333333x. Take half its coefficient (-0.5166666665). Square it (0.2669444443) and add it to both sides. Add '0.2669444443' to each side of the equation. -1.033333333x + 0.2669444443 + x2 = -0.1 + 0.2669444443 Reorder the terms: 0.2669444443 + -1.033333333x + x2 = -0.1 + 0.2669444443 Combine like terms: -0.1 + 0.2669444443 = 0.1669444443 0.2669444443 + -1.033333333x + x2 = 0.1669444443 Factor a perfect square on the left side: (x + -0.5166666665)(x + -0.5166666665) = 0.1669444443 Calculate the square root of the right side: 0.408588356 Break this problem into two subproblems by setting (x + -0.5166666665) equal to 0.408588356 and -0.408588356.Subproblem 1
x + -0.5166666665 = 0.408588356 Simplifying x + -0.5166666665 = 0.408588356 Reorder the terms: -0.5166666665 + x = 0.408588356 Solving -0.5166666665 + x = 0.408588356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5166666665' to each side of the equation. -0.5166666665 + 0.5166666665 + x = 0.408588356 + 0.5166666665 Combine like terms: -0.5166666665 + 0.5166666665 = 0.0000000000 0.0000000000 + x = 0.408588356 + 0.5166666665 x = 0.408588356 + 0.5166666665 Combine like terms: 0.408588356 + 0.5166666665 = 0.9252550225 x = 0.9252550225 Simplifying x = 0.9252550225Subproblem 2
x + -0.5166666665 = -0.408588356 Simplifying x + -0.5166666665 = -0.408588356 Reorder the terms: -0.5166666665 + x = -0.408588356 Solving -0.5166666665 + x = -0.408588356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5166666665' to each side of the equation. -0.5166666665 + 0.5166666665 + x = -0.408588356 + 0.5166666665 Combine like terms: -0.5166666665 + 0.5166666665 = 0.0000000000 0.0000000000 + x = -0.408588356 + 0.5166666665 x = -0.408588356 + 0.5166666665 Combine like terms: -0.408588356 + 0.5166666665 = 0.1080783105 x = 0.1080783105 Simplifying x = 0.1080783105Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9252550225, 0.1080783105}
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