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Simplifying 12x2 + 15x + -35 = 0 Reorder the terms: -35 + 15x + 12x2 = 0 Solving -35 + 15x + 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'. -2.916666667 + 1.25x + x2 = 0 Move the constant term to the right: Add '2.916666667' to each side of the equation. -2.916666667 + 1.25x + 2.916666667 + x2 = 0 + 2.916666667 Reorder the terms: -2.916666667 + 2.916666667 + 1.25x + x2 = 0 + 2.916666667 Combine like terms: -2.916666667 + 2.916666667 = 0.000000000 0.000000000 + 1.25x + x2 = 0 + 2.916666667 1.25x + x2 = 0 + 2.916666667 Combine like terms: 0 + 2.916666667 = 2.916666667 1.25x + x2 = 2.916666667 The x term is 1.25x. Take half its coefficient (0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. 1.25x + 0.390625 + x2 = 2.916666667 + 0.390625 Reorder the terms: 0.390625 + 1.25x + x2 = 2.916666667 + 0.390625 Combine like terms: 2.916666667 + 0.390625 = 3.307291667 0.390625 + 1.25x + x2 = 3.307291667 Factor a perfect square on the left side: (x + 0.625)(x + 0.625) = 3.307291667 Calculate the square root of the right side: 1.81859607 Break this problem into two subproblems by setting (x + 0.625) equal to 1.81859607 and -1.81859607.Subproblem 1
x + 0.625 = 1.81859607 Simplifying x + 0.625 = 1.81859607 Reorder the terms: 0.625 + x = 1.81859607 Solving 0.625 + x = 1.81859607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 1.81859607 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 1.81859607 + -0.625 x = 1.81859607 + -0.625 Combine like terms: 1.81859607 + -0.625 = 1.19359607 x = 1.19359607 Simplifying x = 1.19359607Subproblem 2
x + 0.625 = -1.81859607 Simplifying x + 0.625 = -1.81859607 Reorder the terms: 0.625 + x = -1.81859607 Solving 0.625 + x = -1.81859607 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -1.81859607 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -1.81859607 + -0.625 x = -1.81859607 + -0.625 Combine like terms: -1.81859607 + -0.625 = -2.44359607 x = -2.44359607 Simplifying x = -2.44359607Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.19359607, -2.44359607}
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