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Simplifying 3x2 + -43x + 57 = 0 Reorder the terms: 57 + -43x + 3x2 = 0 Solving 57 + -43x + 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'. 19 + -14.33333333x + x2 = 0 Move the constant term to the right: Add '-19' to each side of the equation. 19 + -14.33333333x + -19 + x2 = 0 + -19 Reorder the terms: 19 + -19 + -14.33333333x + x2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + -14.33333333x + x2 = 0 + -19 -14.33333333x + x2 = 0 + -19 Combine like terms: 0 + -19 = -19 -14.33333333x + x2 = -19 The x term is -14.33333333x. Take half its coefficient (-7.166666665). Square it (51.36111109) and add it to both sides. Add '51.36111109' to each side of the equation. -14.33333333x + 51.36111109 + x2 = -19 + 51.36111109 Reorder the terms: 51.36111109 + -14.33333333x + x2 = -19 + 51.36111109 Combine like terms: -19 + 51.36111109 = 32.36111109 51.36111109 + -14.33333333x + x2 = 32.36111109 Factor a perfect square on the left side: (x + -7.166666665)(x + -7.166666665) = 32.36111109 Calculate the square root of the right side: 5.68868272 Break this problem into two subproblems by setting (x + -7.166666665) equal to 5.68868272 and -5.68868272.Subproblem 1
x + -7.166666665 = 5.68868272 Simplifying x + -7.166666665 = 5.68868272 Reorder the terms: -7.166666665 + x = 5.68868272 Solving -7.166666665 + x = 5.68868272 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.166666665' to each side of the equation. -7.166666665 + 7.166666665 + x = 5.68868272 + 7.166666665 Combine like terms: -7.166666665 + 7.166666665 = 0.000000000 0.000000000 + x = 5.68868272 + 7.166666665 x = 5.68868272 + 7.166666665 Combine like terms: 5.68868272 + 7.166666665 = 12.855349385 x = 12.855349385 Simplifying x = 12.855349385Subproblem 2
x + -7.166666665 = -5.68868272 Simplifying x + -7.166666665 = -5.68868272 Reorder the terms: -7.166666665 + x = -5.68868272 Solving -7.166666665 + x = -5.68868272 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.166666665' to each side of the equation. -7.166666665 + 7.166666665 + x = -5.68868272 + 7.166666665 Combine like terms: -7.166666665 + 7.166666665 = 0.000000000 0.000000000 + x = -5.68868272 + 7.166666665 x = -5.68868272 + 7.166666665 Combine like terms: -5.68868272 + 7.166666665 = 1.477983945 x = 1.477983945 Simplifying x = 1.477983945Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.855349385, 1.477983945}
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