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Simplifying x2 + 2x2 + -49x + -98 = 0 Reorder the terms: -98 + -49x + x2 + 2x2 = 0 Combine like terms: x2 + 2x2 = 3x2 -98 + -49x + 3x2 = 0 Solving -98 + -49x + 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'. -32.66666667 + -16.33333333x + x2 = 0 Move the constant term to the right: Add '32.66666667' to each side of the equation. -32.66666667 + -16.33333333x + 32.66666667 + x2 = 0 + 32.66666667 Reorder the terms: -32.66666667 + 32.66666667 + -16.33333333x + x2 = 0 + 32.66666667 Combine like terms: -32.66666667 + 32.66666667 = 0.00000000 0.00000000 + -16.33333333x + x2 = 0 + 32.66666667 -16.33333333x + x2 = 0 + 32.66666667 Combine like terms: 0 + 32.66666667 = 32.66666667 -16.33333333x + x2 = 32.66666667 The x term is -16.33333333x. Take half its coefficient (-8.166666665). Square it (66.69444442) and add it to both sides. Add '66.69444442' to each side of the equation. -16.33333333x + 66.69444442 + x2 = 32.66666667 + 66.69444442 Reorder the terms: 66.69444442 + -16.33333333x + x2 = 32.66666667 + 66.69444442 Combine like terms: 32.66666667 + 66.69444442 = 99.36111109 66.69444442 + -16.33333333x + x2 = 99.36111109 Factor a perfect square on the left side: (x + -8.166666665)(x + -8.166666665) = 99.36111109 Calculate the square root of the right side: 9.968004368 Break this problem into two subproblems by setting (x + -8.166666665) equal to 9.968004368 and -9.968004368.Subproblem 1
x + -8.166666665 = 9.968004368 Simplifying x + -8.166666665 = 9.968004368 Reorder the terms: -8.166666665 + x = 9.968004368 Solving -8.166666665 + x = 9.968004368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.166666665' to each side of the equation. -8.166666665 + 8.166666665 + x = 9.968004368 + 8.166666665 Combine like terms: -8.166666665 + 8.166666665 = 0.000000000 0.000000000 + x = 9.968004368 + 8.166666665 x = 9.968004368 + 8.166666665 Combine like terms: 9.968004368 + 8.166666665 = 18.134671033 x = 18.134671033 Simplifying x = 18.134671033Subproblem 2
x + -8.166666665 = -9.968004368 Simplifying x + -8.166666665 = -9.968004368 Reorder the terms: -8.166666665 + x = -9.968004368 Solving -8.166666665 + x = -9.968004368 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.166666665' to each side of the equation. -8.166666665 + 8.166666665 + x = -9.968004368 + 8.166666665 Combine like terms: -8.166666665 + 8.166666665 = 0.000000000 0.000000000 + x = -9.968004368 + 8.166666665 x = -9.968004368 + 8.166666665 Combine like terms: -9.968004368 + 8.166666665 = -1.801337703 x = -1.801337703 Simplifying x = -1.801337703Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.134671033, -1.801337703}
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