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Simplifying 9x2 + -12x + -98 = 0 Reorder the terms: -98 + -12x + 9x2 = 0 Solving -98 + -12x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -10.88888889 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '10.88888889' to each side of the equation. -10.88888889 + -1.333333333x + 10.88888889 + x2 = 0 + 10.88888889 Reorder the terms: -10.88888889 + 10.88888889 + -1.333333333x + x2 = 0 + 10.88888889 Combine like terms: -10.88888889 + 10.88888889 = 0.00000000 0.00000000 + -1.333333333x + x2 = 0 + 10.88888889 -1.333333333x + x2 = 0 + 10.88888889 Combine like terms: 0 + 10.88888889 = 10.88888889 -1.333333333x + x2 = 10.88888889 The x term is -1.333333333x. Take half its coefficient (-0.6666666665). Square it (0.4444444442) and add it to both sides. Add '0.4444444442' to each side of the equation. -1.333333333x + 0.4444444442 + x2 = 10.88888889 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 10.88888889 + 0.4444444442 Combine like terms: 10.88888889 + 0.4444444442 = 11.3333333342 0.4444444442 + -1.333333333x + x2 = 11.3333333342 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 11.3333333342 Calculate the square root of the right side: 3.366501646 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 3.366501646 and -3.366501646.Subproblem 1
x + -0.6666666665 = 3.366501646 Simplifying x + -0.6666666665 = 3.366501646 Reorder the terms: -0.6666666665 + x = 3.366501646 Solving -0.6666666665 + x = 3.366501646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = 3.366501646 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 3.366501646 + 0.6666666665 x = 3.366501646 + 0.6666666665 Combine like terms: 3.366501646 + 0.6666666665 = 4.0331683125 x = 4.0331683125 Simplifying x = 4.0331683125Subproblem 2
x + -0.6666666665 = -3.366501646 Simplifying x + -0.6666666665 = -3.366501646 Reorder the terms: -0.6666666665 + x = -3.366501646 Solving -0.6666666665 + x = -3.366501646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6666666665' to each side of the equation. -0.6666666665 + 0.6666666665 + x = -3.366501646 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -3.366501646 + 0.6666666665 x = -3.366501646 + 0.6666666665 Combine like terms: -3.366501646 + 0.6666666665 = -2.6998349795 x = -2.6998349795 Simplifying x = -2.6998349795Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.0331683125, -2.6998349795}
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