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Simplifying 3x2 + 4x + -141 = 0 Reorder the terms: -141 + 4x + 3x2 = 0 Solving -141 + 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'. -47 + 1.333333333x + x2 = 0 Move the constant term to the right: Add '47' to each side of the equation. -47 + 1.333333333x + 47 + x2 = 0 + 47 Reorder the terms: -47 + 47 + 1.333333333x + x2 = 0 + 47 Combine like terms: -47 + 47 = 0 0 + 1.333333333x + x2 = 0 + 47 1.333333333x + x2 = 0 + 47 Combine like terms: 0 + 47 = 47 1.333333333x + x2 = 47 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 = 47 + 0.4444444442 Reorder the terms: 0.4444444442 + 1.333333333x + x2 = 47 + 0.4444444442 Combine like terms: 47 + 0.4444444442 = 47.4444444442 0.4444444442 + 1.333333333x + x2 = 47.4444444442 Factor a perfect square on the left side: (x + 0.6666666665)(x + 0.6666666665) = 47.4444444442 Calculate the square root of the right side: 6.887992773 Break this problem into two subproblems by setting (x + 0.6666666665) equal to 6.887992773 and -6.887992773.Subproblem 1
x + 0.6666666665 = 6.887992773 Simplifying x + 0.6666666665 = 6.887992773 Reorder the terms: 0.6666666665 + x = 6.887992773 Solving 0.6666666665 + x = 6.887992773 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 = 6.887992773 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = 6.887992773 + -0.6666666665 x = 6.887992773 + -0.6666666665 Combine like terms: 6.887992773 + -0.6666666665 = 6.2213261065 x = 6.2213261065 Simplifying x = 6.2213261065Subproblem 2
x + 0.6666666665 = -6.887992773 Simplifying x + 0.6666666665 = -6.887992773 Reorder the terms: 0.6666666665 + x = -6.887992773 Solving 0.6666666665 + x = -6.887992773 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 = -6.887992773 + -0.6666666665 Combine like terms: 0.6666666665 + -0.6666666665 = 0.0000000000 0.0000000000 + x = -6.887992773 + -0.6666666665 x = -6.887992773 + -0.6666666665 Combine like terms: -6.887992773 + -0.6666666665 = -7.5546594395 x = -7.5546594395 Simplifying x = -7.5546594395Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.2213261065, -7.5546594395}
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