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Simplifying 3x2 + -31x + 30 = 0 Reorder the terms: 30 + -31x + 3x2 = 0 Solving 30 + -31x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 10 + -10.33333333x + x2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + -10.33333333x + -10 + x2 = 0 + -10 Reorder the terms: 10 + -10 + -10.33333333x + x2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -10.33333333x + x2 = 0 + -10 -10.33333333x + x2 = 0 + -10 Combine like terms: 0 + -10 = -10 -10.33333333x + x2 = -10 The x term is -10.33333333x. Take half its coefficient (-5.166666665). Square it (26.69444443) and add it to both sides. Add '26.69444443' to each side of the equation. -10.33333333x + 26.69444443 + x2 = -10 + 26.69444443 Reorder the terms: 26.69444443 + -10.33333333x + x2 = -10 + 26.69444443 Combine like terms: -10 + 26.69444443 = 16.69444443 26.69444443 + -10.33333333x + x2 = 16.69444443 Factor a perfect square on the left side: (x + -5.166666665)(x + -5.166666665) = 16.69444443 Calculate the square root of the right side: 4.085883556 Break this problem into two subproblems by setting (x + -5.166666665) equal to 4.085883556 and -4.085883556.Subproblem 1
x + -5.166666665 = 4.085883556 Simplifying x + -5.166666665 = 4.085883556 Reorder the terms: -5.166666665 + x = 4.085883556 Solving -5.166666665 + x = 4.085883556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.166666665' to each side of the equation. -5.166666665 + 5.166666665 + x = 4.085883556 + 5.166666665 Combine like terms: -5.166666665 + 5.166666665 = 0.000000000 0.000000000 + x = 4.085883556 + 5.166666665 x = 4.085883556 + 5.166666665 Combine like terms: 4.085883556 + 5.166666665 = 9.252550221 x = 9.252550221 Simplifying x = 9.252550221Subproblem 2
x + -5.166666665 = -4.085883556 Simplifying x + -5.166666665 = -4.085883556 Reorder the terms: -5.166666665 + x = -4.085883556 Solving -5.166666665 + x = -4.085883556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.166666665' to each side of the equation. -5.166666665 + 5.166666665 + x = -4.085883556 + 5.166666665 Combine like terms: -5.166666665 + 5.166666665 = 0.000000000 0.000000000 + x = -4.085883556 + 5.166666665 x = -4.085883556 + 5.166666665 Combine like terms: -4.085883556 + 5.166666665 = 1.080783109 x = 1.080783109 Simplifying x = 1.080783109Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.252550221, 1.080783109}
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