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Simplifying 9x2 + 12x + -1(-3.35) = 0 Multiply -1 * -3.35 9x2 + 12x + 3.35 = 0 Reorder the terms: 3.35 + 12x + 9x2 = 0 Solving 3.35 + 12x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.3722222222 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '-0.3722222222' to each side of the equation. 0.3722222222 + 1.333333333x + -0.3722222222 + x2 = 0 + -0.3722222222 Reorder the terms: 0.3722222222 + -0.3722222222 + 1.333333333x + x2 = 0 + -0.3722222222 Combine like terms: 0.3722222222 + -0.3722222222 = 0.0000000000 0.0000000000 + 1.333333333x + x2 = 0 + -0.3722222222 1.333333333x + x2 = 0 + -0.3722222222 Combine like terms: 0 + -0.3722222222 = -0.3722222222 1.333333333x + x2 = -0.3722222222 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 = -0.3722222222 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = -0.3722222222 + 0.4444444442 Combine like terms: -0.3722222222 + 0.4444444442 = 0.072222222 0.4444444442 + 1.333333333x + x2 = 0.072222222 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 0.072222222 Calculate the square root of the right side: 0.268741925 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 0.268741925 and -0.268741925.Subproblem 1
x + 0.6666666665 = 0.268741925 Simplifying x + 0.6666666665 = 0.268741925 Reorder the terms: 0.6666666665 + x = 0.268741925 Solving 0.6666666665 + x = 0.268741925 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 = 0.268741925 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 0.268741925 + -0.6666666665 x = 0.268741925 + -0.6666666665 Combine like terms: 0.268741925 + -0.6666666665 = -0.3979247415 x = -0.3979247415 Simplifying x = -0.3979247415Subproblem 2
x + 0.6666666665 = -0.268741925 Simplifying x + 0.6666666665 = -0.268741925 Reorder the terms: 0.6666666665 + x = -0.268741925 Solving 0.6666666665 + x = -0.268741925 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 = -0.268741925 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -0.268741925 + -0.6666666665 x = -0.268741925 + -0.6666666665 Combine like terms: -0.268741925 + -0.6666666665 = -0.9354085915 x = -0.9354085915 Simplifying x = -0.9354085915Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.3979247415, -0.9354085915}
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