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Simplifying 9x2 + -12x = 8 Reorder the terms: -12x + 9x2 = 8 Solving -12x + 9x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -12x + 9x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + -1.333333333x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + -1.333333333x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + -1.333333333x + x2 = 0 + 0.8888888889 -1.333333333x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 -1.333333333x + x2 = 0.8888888889 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 = 0.8888888889 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 0.8888888889 + 0.4444444442 Combine like terms: 0.8888888889 + 0.4444444442 = 1.3333333331 0.4444444442 + -1.333333333x + x2 = 1.3333333331 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 1.3333333331 Calculate the square root of the right side: 1.154700538 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 1.154700538 and -1.154700538.Subproblem 1
x + -0.6666666665 = 1.154700538 Simplifying x + -0.6666666665 = 1.154700538 Reorder the terms: -0.6666666665 + x = 1.154700538 Solving -0.6666666665 + x = 1.154700538 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 = 1.154700538 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 1.154700538 + 0.6666666665 x = 1.154700538 + 0.6666666665 Combine like terms: 1.154700538 + 0.6666666665 = 1.8213672045 x = 1.8213672045 Simplifying x = 1.8213672045Subproblem 2
x + -0.6666666665 = -1.154700538 Simplifying x + -0.6666666665 = -1.154700538 Reorder the terms: -0.6666666665 + x = -1.154700538 Solving -0.6666666665 + x = -1.154700538 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 = -1.154700538 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -1.154700538 + 0.6666666665 x = -1.154700538 + 0.6666666665 Combine like terms: -1.154700538 + 0.6666666665 = -0.4880338715 x = -0.4880338715 Simplifying x = -0.4880338715Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.8213672045, -0.4880338715}
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