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Simplifying 12x2 + -13x + -35 = 10 Reorder the terms: -35 + -13x + 12x2 = 10 Solving -35 + -13x + 12x2 = 10 Solving for variable 'x'. Reorder the terms: -35 + -10 + -13x + 12x2 = 10 + -10 Combine like terms: -35 + -10 = -45 -45 + -13x + 12x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -45 + -13x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -3.75 + -1.083333333x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -1.083333333x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -1.083333333x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -1.083333333x + x2 = 0 + 3.75 -1.083333333x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -1.083333333x + x2 = 3.75 The x term is -1.083333333x. Take half its coefficient (-0.5416666665). Square it (0.2934027776) and add it to both sides. Add '0.2934027776' to each side of the equation. -1.083333333x + 0.2934027776 + x2 = 3.75 + 0.2934027776 Reorder the terms: 0.2934027776 + -1.083333333x + x2 = 3.75 + 0.2934027776 Combine like terms: 3.75 + 0.2934027776 = 4.0434027776 0.2934027776 + -1.083333333x + x2 = 4.0434027776 Factor a perfect square on the left side: (x + -0.5416666665)(x + -0.5416666665) = 4.0434027776 Calculate the square root of the right side: 2.010821419 Break this problem into two subproblems by setting (x + -0.5416666665) equal to 2.010821419 and -2.010821419.Subproblem 1
x + -0.5416666665 = 2.010821419 Simplifying x + -0.5416666665 = 2.010821419 Reorder the terms: -0.5416666665 + x = 2.010821419 Solving -0.5416666665 + x = 2.010821419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5416666665' to each side of the equation. -0.5416666665 + 0.5416666665 + x = 2.010821419 + 0.5416666665 Combine like terms: -0.5416666665 + 0.5416666665 = 0.0000000000 0.0000000000 + x = 2.010821419 + 0.5416666665 x = 2.010821419 + 0.5416666665 Combine like terms: 2.010821419 + 0.5416666665 = 2.5524880855 x = 2.5524880855 Simplifying x = 2.5524880855Subproblem 2
x + -0.5416666665 = -2.010821419 Simplifying x + -0.5416666665 = -2.010821419 Reorder the terms: -0.5416666665 + x = -2.010821419 Solving -0.5416666665 + x = -2.010821419 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5416666665' to each side of the equation. -0.5416666665 + 0.5416666665 + x = -2.010821419 + 0.5416666665 Combine like terms: -0.5416666665 + 0.5416666665 = 0.0000000000 0.0000000000 + x = -2.010821419 + 0.5416666665 x = -2.010821419 + 0.5416666665 Combine like terms: -2.010821419 + 0.5416666665 = -1.4691547525 x = -1.4691547525 Simplifying x = -1.4691547525Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.5524880855, -1.4691547525}
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