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Simplifying 3x2 + 4x + -72 = 0 Reorder the terms: -72 + 4x + 3x2 = 0 Solving -72 + 4x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -24 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '24' to each side of the equation. -24 + 1.333333333x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + 1.333333333x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + 1.333333333x + x2 = 0 + 24 1.333333333x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 1.333333333x + x2 = 24 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 = 24 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 24 + 0.4444444442 Combine like terms: 24 + 0.4444444442 = 24.4444444442 0.4444444442 + 1.333333333x + x2 = 24.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 24.4444444442 Calculate the square root of the right side: 4.944132325 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 4.944132325 and -4.944132325.Subproblem 1
x + 0.6666666665 = 4.944132325 Simplifying x + 0.6666666665 = 4.944132325 Reorder the terms: 0.6666666665 + x = 4.944132325 Solving 0.6666666665 + x = 4.944132325 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 = 4.944132325 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 4.944132325 + -0.6666666665 x = 4.944132325 + -0.6666666665 Combine like terms: 4.944132325 + -0.6666666665 = 4.2774656585 x = 4.2774656585 Simplifying x = 4.2774656585Subproblem 2
x + 0.6666666665 = -4.944132325 Simplifying x + 0.6666666665 = -4.944132325 Reorder the terms: 0.6666666665 + x = -4.944132325 Solving 0.6666666665 + x = -4.944132325 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 = -4.944132325 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -4.944132325 + -0.6666666665 x = -4.944132325 + -0.6666666665 Combine like terms: -4.944132325 + -0.6666666665 = -5.6107989915 x = -5.6107989915 Simplifying x = -5.6107989915Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.2774656585, -5.6107989915}
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