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Simplifying (-12x2 + 19x + -6) = 0 Reorder the terms: (-6 + 19x + -12x2) = 0 Remove parenthesis around (-6 + 19x + -12x2) -6 + 19x + -12x2 = 0 Solving -6 + 19x + -12x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -12 the coefficient of the squared term: Divide each side by '-12'. 0.5 + -1.583333333x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -1.583333333x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -1.583333333x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -1.583333333x + x2 = 0 + -0.5 -1.583333333x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -1.583333333x + x2 = -0.5 The x term is -1.583333333x. Take half its coefficient (-0.7916666665). Square it (0.6267361108) and add it to both sides. Add '0.6267361108' to each side of the equation. -1.583333333x + 0.6267361108 + x2 = -0.5 + 0.6267361108 Reorder the terms: 0.6267361108 + -1.583333333x + x2 = -0.5 + 0.6267361108 Combine like terms: -0.5 + 0.6267361108 = 0.1267361108 0.6267361108 + -1.583333333x + x2 = 0.1267361108 Factor a perfect square on the left side: (x + -0.7916666665)(x + -0.7916666665) = 0.1267361108 Calculate the square root of the right side: 0.356000156 Break this problem into two subproblems by setting (x + -0.7916666665) equal to 0.356000156 and -0.356000156.Subproblem 1
x + -0.7916666665 = 0.356000156 Simplifying x + -0.7916666665 = 0.356000156 Reorder the terms: -0.7916666665 + x = 0.356000156 Solving -0.7916666665 + x = 0.356000156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7916666665' to each side of the equation. -0.7916666665 + 0.7916666665 + x = 0.356000156 + 0.7916666665 Combine like terms: -0.7916666665 + 0.7916666665 = 0.0000000000 0.0000000000 + x = 0.356000156 + 0.7916666665 x = 0.356000156 + 0.7916666665 Combine like terms: 0.356000156 + 0.7916666665 = 1.1476668225 x = 1.1476668225 Simplifying x = 1.1476668225Subproblem 2
x + -0.7916666665 = -0.356000156 Simplifying x + -0.7916666665 = -0.356000156 Reorder the terms: -0.7916666665 + x = -0.356000156 Solving -0.7916666665 + x = -0.356000156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7916666665' to each side of the equation. -0.7916666665 + 0.7916666665 + x = -0.356000156 + 0.7916666665 Combine like terms: -0.7916666665 + 0.7916666665 = 0.0000000000 0.0000000000 + x = -0.356000156 + 0.7916666665 x = -0.356000156 + 0.7916666665 Combine like terms: -0.356000156 + 0.7916666665 = 0.4356665105 x = 0.4356665105 Simplifying x = 0.4356665105Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1476668225, 0.4356665105}
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