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Simplifying 9x2 + 12x + 4 = 24 Reorder the terms: 4 + 12x + 9x2 = 24 Solving 4 + 12x + 9x2 = 24 Solving for variable 'x'. Reorder the terms: 4 + -24 + 12x + 9x2 = 24 + -24 Combine like terms: 4 + -24 = -20 -20 + 12x + 9x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -20 + 12x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.222222222 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + 1.333333333x + 2.222222222 + x2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + 1.333333333x + x2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + 1.333333333x + x2 = 0 + 2.222222222 1.333333333x + x2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 1.333333333x + x2 = 2.222222222 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 = 2.222222222 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 2.222222222 + 0.4444444442 Combine like terms: 2.222222222 + 0.4444444442 = 2.6666666662 0.4444444442 + 1.333333333x + x2 = 2.6666666662 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 2.6666666662 Calculate the square root of the right side: 1.632993162 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 1.632993162 and -1.632993162.Subproblem 1
x + 0.6666666665 = 1.632993162 Simplifying x + 0.6666666665 = 1.632993162 Reorder the terms: 0.6666666665 + x = 1.632993162 Solving 0.6666666665 + x = 1.632993162 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 = 1.632993162 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 1.632993162 + -0.6666666665 x = 1.632993162 + -0.6666666665 Combine like terms: 1.632993162 + -0.6666666665 = 0.9663264955 x = 0.9663264955 Simplifying x = 0.9663264955Subproblem 2
x + 0.6666666665 = -1.632993162 Simplifying x + 0.6666666665 = -1.632993162 Reorder the terms: 0.6666666665 + x = -1.632993162 Solving 0.6666666665 + x = -1.632993162 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 = -1.632993162 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -1.632993162 + -0.6666666665 x = -1.632993162 + -0.6666666665 Combine like terms: -1.632993162 + -0.6666666665 = -2.2996598285 x = -2.2996598285 Simplifying x = -2.2996598285Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.9663264955, -2.2996598285}
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