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Simplifying (9x + -6)(9x + -6) + -7 = 0 Reorder the terms: (-6 + 9x)(9x + -6) + -7 = 0 Reorder the terms: (-6 + 9x)(-6 + 9x) + -7 = 0 Multiply (-6 + 9x) * (-6 + 9x) (-6(-6 + 9x) + 9x * (-6 + 9x)) + -7 = 0 ((-6 * -6 + 9x * -6) + 9x * (-6 + 9x)) + -7 = 0 ((36 + -54x) + 9x * (-6 + 9x)) + -7 = 0 (36 + -54x + (-6 * 9x + 9x * 9x)) + -7 = 0 (36 + -54x + (-54x + 81x2)) + -7 = 0 Combine like terms: -54x + -54x = -108x (36 + -108x + 81x2) + -7 = 0 Reorder the terms: 36 + -7 + -108x + 81x2 = 0 Combine like terms: 36 + -7 = 29 29 + -108x + 81x2 = 0 Solving 29 + -108x + 81x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 81 the coefficient of the squared term: Divide each side by '81'. 0.3580246914 + -1.333333333x + x2 = 0 Move the constant term to the right: Add '-0.3580246914' to each side of the equation. 0.3580246914 + -1.333333333x + -0.3580246914 + x2 = 0 + -0.3580246914 Reorder the terms: 0.3580246914 + -0.3580246914 + -1.333333333x + x2 = 0 + -0.3580246914 Combine like terms: 0.3580246914 + -0.3580246914 = 0.0000000000 0.0000000000 + -1.333333333x + x2 = 0 + -0.3580246914 -1.333333333x + x2 = 0 + -0.3580246914 Combine like terms: 0 + -0.3580246914 = -0.3580246914 -1.333333333x + x2 = -0.3580246914 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 = -0.3580246914 + 0.4444444442 Reorder the terms: 0.4444444442 + -1.333333333x + x2 = -0.3580246914 + 0.4444444442 Combine like terms: -0.3580246914 + 0.4444444442 = 0.0864197528 0.4444444442 + -1.333333333x + x2 = 0.0864197528 Factor a perfect square on the left side: (x + -0.6666666665)(x + -0.6666666665) = 0.0864197528 Calculate the square root of the right side: 0.293972367 Break this problem into two subproblems by setting (x + -0.6666666665) equal to 0.293972367 and -0.293972367.Subproblem 1
x + -0.6666666665 = 0.293972367 Simplifying x + -0.6666666665 = 0.293972367 Reorder the terms: -0.6666666665 + x = 0.293972367 Solving -0.6666666665 + x = 0.293972367 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 = 0.293972367 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = 0.293972367 + 0.6666666665 x = 0.293972367 + 0.6666666665 Combine like terms: 0.293972367 + 0.6666666665 = 0.9606390335 x = 0.9606390335 Simplifying x = 0.9606390335Subproblem 2
x + -0.6666666665 = -0.293972367 Simplifying x + -0.6666666665 = -0.293972367 Reorder the terms: -0.6666666665 + x = -0.293972367 Solving -0.6666666665 + x = -0.293972367 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 = -0.293972367 + 0.6666666665 Combine like terms: -0.6666666665 + 0.6666666665 = 0.0000000000 0.0000000000 + x = -0.293972367 + 0.6666666665 x = -0.293972367 + 0.6666666665 Combine like terms: -0.293972367 + 0.6666666665 = 0.3726942995 x = 0.3726942995 Simplifying x = 0.3726942995Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9606390335, 0.3726942995}
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