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Simplifying 0 = 3x2 + -4x + -9 Reorder the terms: 0 = -9 + -4x + 3x2 Solving 0 = -9 + -4x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 9 = 9 9 + 4x + -3x2 = -9 + -4x + 3x2 + 9 + 4x + -3x2 Reorder the terms: 9 + 4x + -3x2 = -9 + 9 + -4x + 4x + 3x2 + -3x2 Combine like terms: -9 + 9 = 0 9 + 4x + -3x2 = 0 + -4x + 4x + 3x2 + -3x2 9 + 4x + -3x2 = -4x + 4x + 3x2 + -3x2 Combine like terms: -4x + 4x = 0 9 + 4x + -3x2 = 0 + 3x2 + -3x2 9 + 4x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 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 = 2.5225881205 x = 2.5225881205 Simplifying x = 2.5225881205Subproblem 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 = -1.1892547875 x = -1.1892547875 Simplifying x = -1.1892547875Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5225881205, -1.1892547875}
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