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Simplifying 9x2 + 12x = 27 Reorder the terms: 12x + 9x2 = 27 Solving 12x + 9x2 = 27 Solving for variable 'x'. Reorder the terms: -27 + 12x + 9x2 = 27 + -27 Combine like terms: 27 + -27 = 0 -27 + 12x + 9x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + 4x + 3x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-9 + 4x + 3x2)' equal to zero and attempt to solve: Simplifying -9 + 4x + 3x2 = 0 Solving -9 + 4x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -3 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 1.333333333x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 1.333333333x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 1.333333333x + x2 = 0 + 3 1.333333333x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 1.333333333x + x2 = 3 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 = 3 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 3 + 0.4444444442 Combine like terms: 3 + 0.4444444442 = 3.4444444442 0.4444444442 + 1.333333333x + x2 = 3.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 3.4444444442 Calculate the square root of the right side: 1.855921454 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 1.855921454 and -1.855921454.Subproblem 1
x + 0.6666666665 = 1.855921454 Simplifying x + 0.6666666665 = 1.855921454 Reorder the terms: 0.6666666665 + x = 1.855921454 Solving 0.6666666665 + x = 1.855921454 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 = 1.855921454 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 1.855921454 + -0.6666666665 x = 1.855921454 + -0.6666666665 Combine like terms: 1.855921454 + -0.6666666665 = 1.1892547875 x = 1.1892547875 Simplifying x = 1.1892547875Subproblem 2
x + 0.6666666665 = -1.855921454 Simplifying x + 0.6666666665 = -1.855921454 Reorder the terms: 0.6666666665 + x = -1.855921454 Solving 0.6666666665 + x = -1.855921454 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 = -1.855921454 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -1.855921454 + -0.6666666665 x = -1.855921454 + -0.6666666665 Combine like terms: -1.855921454 + -0.6666666665 = -2.5225881205 x = -2.5225881205 Simplifying x = -2.5225881205Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1892547875, -2.5225881205}Solution
x = {1.1892547875, -2.5225881205}
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