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Simplifying 24x2 + 32x + -33 = 0 Reorder the terms: -33 + 32x + 24x2 = 0 Solving -33 + 32x + 24x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 24 the coefficient of the squared term: Divide each side by '24'. -1.375 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '1.375' to each side of the equation. -1.375 + 1.333333333x + 1.375 + x2 = 0 + 1.375 Reorder the terms: -1.375 + 1.375 + 1.333333333x + x2 = 0 + 1.375 Combine like terms: -1.375 + 1.375 = 0.000 0.000 + 1.333333333x + x2 = 0 + 1.375 1.333333333x + x2 = 0 + 1.375 Combine like terms: 0 + 1.375 = 1.375 1.333333333x + x2 = 1.375 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 = 1.375 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 1.375 + 0.4444444442 Combine like terms: 1.375 + 0.4444444442 = 1.8194444442 0.4444444442 + 1.333333333x + x2 = 1.8194444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 1.8194444442 Calculate the square root of the right side: 1.348867838 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 1.348867838 and -1.348867838.Subproblem 1
x + 0.6666666665 = 1.348867838 Simplifying x + 0.6666666665 = 1.348867838 Reorder the terms: 0.6666666665 + x = 1.348867838 Solving 0.6666666665 + x = 1.348867838 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 = 1.348867838 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 1.348867838 + -0.6666666665 x = 1.348867838 + -0.6666666665 Combine like terms: 1.348867838 + -0.6666666665 = 0.6822011715 x = 0.6822011715 Simplifying x = 0.6822011715Subproblem 2
x + 0.6666666665 = -1.348867838 Simplifying x + 0.6666666665 = -1.348867838 Reorder the terms: 0.6666666665 + x = -1.348867838 Solving 0.6666666665 + x = -1.348867838 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 = -1.348867838 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -1.348867838 + -0.6666666665 x = -1.348867838 + -0.6666666665 Combine like terms: -1.348867838 + -0.6666666665 = -2.0155345045 x = -2.0155345045 Simplifying x = -2.0155345045Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6822011715, -2.0155345045}
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