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Simplifying 3x2 + -49x + -21 = 0 Reorder the terms: -21 + -49x + 3x2 = 0 Solving -21 + -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'. -7 + -16.33333333x + x2 = 0 Move the constant term to the right: Add '7' to each side of the equation. -7 + -16.33333333x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -16.33333333x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -16.33333333x + x2 = 0 + 7 -16.33333333x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -16.33333333x + x2 = 7 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 = 7 + 66.69444442 Reorder the terms: 66.69444442 + -16.33333333x + x2 = 7 + 66.69444442 Combine like terms: 7 + 66.69444442 = 73.69444442 66.69444442 + -16.33333333x + x2 = 73.69444442 Factor a perfect square on the left side: (x + -8.166666665)(x + -8.166666665) = 73.69444442 Calculate the square root of the right side: 8.584546838 Break this problem into two subproblems by setting (x + -8.166666665) equal to 8.584546838 and -8.584546838.Subproblem 1
x + -8.166666665 = 8.584546838 Simplifying x + -8.166666665 = 8.584546838 Reorder the terms: -8.166666665 + x = 8.584546838 Solving -8.166666665 + x = 8.584546838 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 = 8.584546838 + 8.166666665 Combine like terms: -8.166666665 + 8.166666665 = 0.000000000 0.000000000 + x = 8.584546838 + 8.166666665 x = 8.584546838 + 8.166666665 Combine like terms: 8.584546838 + 8.166666665 = 16.751213503 x = 16.751213503 Simplifying x = 16.751213503Subproblem 2
x + -8.166666665 = -8.584546838 Simplifying x + -8.166666665 = -8.584546838 Reorder the terms: -8.166666665 + x = -8.584546838 Solving -8.166666665 + x = -8.584546838 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 = -8.584546838 + 8.166666665 Combine like terms: -8.166666665 + 8.166666665 = 0.000000000 0.000000000 + x = -8.584546838 + 8.166666665 x = -8.584546838 + 8.166666665 Combine like terms: -8.584546838 + 8.166666665 = -0.417880173 x = -0.417880173 Simplifying x = -0.417880173Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.751213503, -0.417880173}
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