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Simplifying -12x2 + -19x + 36 = 0 Reorder the terms: 36 + -19x + -12x2 = 0 Solving 36 + -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'. -3 + 1.583333333x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + 1.583333333x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 1.583333333x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 1.583333333x + x2 = 0 + 3 1.583333333x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 1.583333333x + x2 = 3 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 = 3 + 0.6267361108 Reorder the terms: 0.6267361108 + 1.583333333x + x2 = 3 + 0.6267361108 Combine like terms: 3 + 0.6267361108 = 3.6267361108 0.6267361108 + 1.583333333x + x2 = 3.6267361108 Factor a perfect square on the left side: (x + 0.7916666665)(x + 0.7916666665) = 3.6267361108 Calculate the square root of the right side: 1.904399147 Break this problem into two subproblems by setting (x + 0.7916666665) equal to 1.904399147 and -1.904399147.Subproblem 1
x + 0.7916666665 = 1.904399147 Simplifying x + 0.7916666665 = 1.904399147 Reorder the terms: 0.7916666665 + x = 1.904399147 Solving 0.7916666665 + x = 1.904399147 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 = 1.904399147 + -0.7916666665 Combine like terms: 0.7916666665 + -0.7916666665 = 0.0000000000 0.0000000000 + x = 1.904399147 + -0.7916666665 x = 1.904399147 + -0.7916666665 Combine like terms: 1.904399147 + -0.7916666665 = 1.1127324805 x = 1.1127324805 Simplifying x = 1.1127324805Subproblem 2
x + 0.7916666665 = -1.904399147 Simplifying x + 0.7916666665 = -1.904399147 Reorder the terms: 0.7916666665 + x = -1.904399147 Solving 0.7916666665 + x = -1.904399147 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 = -1.904399147 + -0.7916666665 Combine like terms: 0.7916666665 + -0.7916666665 = 0.0000000000 0.0000000000 + x = -1.904399147 + -0.7916666665 x = -1.904399147 + -0.7916666665 Combine like terms: -1.904399147 + -0.7916666665 = -2.6960658135 x = -2.6960658135 Simplifying x = -2.6960658135Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1127324805, -2.6960658135}
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