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Simplifying 3x2 + 4x + -174 = 0 Reorder the terms: -174 + 4x + 3x2 = 0 Solving -174 + 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'. -58 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '58' to each side of the equation. -58 + 1.333333333x + 58 + x2 = 0 + 58 Reorder the terms: -58 + 58 + 1.333333333x + x2 = 0 + 58 Combine like terms: -58 + 58 = 0 0 + 1.333333333x + x2 = 0 + 58 1.333333333x + x2 = 0 + 58 Combine like terms: 0 + 58 = 58 1.333333333x + x2 = 58 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 = 58 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 58 + 0.4444444442 Combine like terms: 58 + 0.4444444442 = 58.4444444442 0.4444444442 + 1.333333333x + x2 = 58.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 58.4444444442 Calculate the square root of the right side: 7.644896627 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 7.644896627 and -7.644896627.Subproblem 1
x + 0.6666666665 = 7.644896627 Simplifying x + 0.6666666665 = 7.644896627 Reorder the terms: 0.6666666665 + x = 7.644896627 Solving 0.6666666665 + x = 7.644896627 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 = 7.644896627 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 7.644896627 + -0.6666666665 x = 7.644896627 + -0.6666666665 Combine like terms: 7.644896627 + -0.6666666665 = 6.9782299605 x = 6.9782299605 Simplifying x = 6.9782299605Subproblem 2
x + 0.6666666665 = -7.644896627 Simplifying x + 0.6666666665 = -7.644896627 Reorder the terms: 0.6666666665 + x = -7.644896627 Solving 0.6666666665 + x = -7.644896627 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 = -7.644896627 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -7.644896627 + -0.6666666665 x = -7.644896627 + -0.6666666665 Combine like terms: -7.644896627 + -0.6666666665 = -8.3115632935 x = -8.3115632935 Simplifying x = -8.3115632935Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.9782299605, -8.3115632935}
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