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Simplifying 9x2 + 12x + 4 = 6720 Reorder the terms: 4 + 12x + 9x2 = 6720 Solving 4 + 12x + 9x2 = 6720 Solving for variable 'x'. Reorder the terms: 4 + -6720 + 12x + 9x2 = 6720 + -6720 Combine like terms: 4 + -6720 = -6716 -6716 + 12x + 9x2 = 6720 + -6720 Combine like terms: 6720 + -6720 = 0 -6716 + 12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -746.2222222 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '746.2222222' to each side of the equation. -746.2222222 + 1.333333333x + 746.2222222 + x2 = 0 + 746.2222222 Reorder the terms: -746.2222222 + 746.2222222 + 1.333333333x + x2 = 0 + 746.2222222 Combine like terms: -746.2222222 + 746.2222222 = 0.0000000 0.0000000 + 1.333333333x + x2 = 0 + 746.2222222 1.333333333x + x2 = 0 + 746.2222222 Combine like terms: 0 + 746.2222222 = 746.2222222 1.333333333x + x2 = 746.2222222 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 = 746.2222222 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 746.2222222 + 0.4444444442 Combine like terms: 746.2222222 + 0.4444444442 = 746.6666666442 0.4444444442 + 1.333333333x + x2 = 746.6666666442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 746.6666666442 Calculate the square root of the right side: 27.325202042 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 27.325202042 and -27.325202042.Subproblem 1
x + 0.6666666665 = 27.325202042 Simplifying x + 0.6666666665 = 27.325202042 Reorder the terms: 0.6666666665 + x = 27.325202042 Solving 0.6666666665 + x = 27.325202042 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 = 27.325202042 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 27.325202042 + -0.6666666665 x = 27.325202042 + -0.6666666665 Combine like terms: 27.325202042 + -0.6666666665 = 26.6585353755 x = 26.6585353755 Simplifying x = 26.6585353755Subproblem 2
x + 0.6666666665 = -27.325202042 Simplifying x + 0.6666666665 = -27.325202042 Reorder the terms: 0.6666666665 + x = -27.325202042 Solving 0.6666666665 + x = -27.325202042 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 = -27.325202042 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -27.325202042 + -0.6666666665 x = -27.325202042 + -0.6666666665 Combine like terms: -27.325202042 + -0.6666666665 = -27.9918687085 x = -27.9918687085 Simplifying x = -27.9918687085Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.6585353755, -27.9918687085}
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