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Simplifying 9x2 + -12x + 4 = 63 Reorder the terms: 4 + -12x + 9x2 = 63 Solving 4 + -12x + 9x2 = 63 Solving for variable 'x'. Reorder the terms: 4 + -63 + -12x + 9x2 = 63 + -63 Combine like terms: 4 + -63 = -59 -59 + -12x + 9x2 = 63 + -63 Combine like terms: 63 + -63 = 0 -59 + -12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -6.555555556 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '6.555555556' to each side of the equation. -6.555555556 + -1.333333333x + 6.555555556 + x2 = 0 + 6.555555556 Reorder the terms: -6.555555556 + 6.555555556 + -1.333333333x + x2 = 0 + 6.555555556 Combine like terms: -6.555555556 + 6.555555556 = 0.000000000 0.000000000 + -1.333333333x + x2 = 0 + 6.555555556 -1.333333333x + x2 = 0 + 6.555555556 Combine like terms: 0 + 6.555555556 = 6.555555556 -1.333333333x + x2 = 6.555555556 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 = 6.555555556 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = 6.555555556 + 0.4444444442 Combine like terms: 6.555555556 + 0.4444444442 = 7.0000000002 0.4444444442 + -1.333333333x + x2 = 7.0000000002 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 7.0000000002 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 2.645751311 and -2.645751311.Subproblem 1
x + -0.6666666665 = 2.645751311 Simplifying x + -0.6666666665 = 2.645751311 Reorder the terms: -0.6666666665 + x = 2.645751311 Solving -0.6666666665 + x = 2.645751311 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 = 2.645751311 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 2.645751311 + 0.6666666665 x = 2.645751311 + 0.6666666665 Combine like terms: 2.645751311 + 0.6666666665 = 3.3124179775 x = 3.3124179775 Simplifying x = 3.3124179775Subproblem 2
x + -0.6666666665 = -2.645751311 Simplifying x + -0.6666666665 = -2.645751311 Reorder the terms: -0.6666666665 + x = -2.645751311 Solving -0.6666666665 + x = -2.645751311 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 = -2.645751311 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -2.645751311 + 0.6666666665 x = -2.645751311 + 0.6666666665 Combine like terms: -2.645751311 + 0.6666666665 = -1.9790846445 x = -1.9790846445 Simplifying x = -1.9790846445Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.3124179775, -1.9790846445}
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