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Simplifying x2 + 3x + -2012 = 0 Reorder the terms: -2012 + 3x + x2 = 0 Solving -2012 + 3x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2012' to each side of the equation. -2012 + 3x + 2012 + x2 = 0 + 2012 Reorder the terms: -2012 + 2012 + 3x + x2 = 0 + 2012 Combine like terms: -2012 + 2012 = 0 0 + 3x + x2 = 0 + 2012 3x + x2 = 0 + 2012 Combine like terms: 0 + 2012 = 2012 3x + x2 = 2012 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 2012 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 2012 + 2.25 Combine like terms: 2012 + 2.25 = 2014.25 2.25 + 3x + x2 = 2014.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 2014.25 Calculate the square root of the right side: 44.880396611 Break this problem into two subproblems by setting (x + 1.5) equal to 44.880396611 and -44.880396611.Subproblem 1
x + 1.5 = 44.880396611 Simplifying x + 1.5 = 44.880396611 Reorder the terms: 1.5 + x = 44.880396611 Solving 1.5 + x = 44.880396611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 44.880396611 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 44.880396611 + -1.5 x = 44.880396611 + -1.5 Combine like terms: 44.880396611 + -1.5 = 43.380396611 x = 43.380396611 Simplifying x = 43.380396611Subproblem 2
x + 1.5 = -44.880396611 Simplifying x + 1.5 = -44.880396611 Reorder the terms: 1.5 + x = -44.880396611 Solving 1.5 + x = -44.880396611 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -44.880396611 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -44.880396611 + -1.5 x = -44.880396611 + -1.5 Combine like terms: -44.880396611 + -1.5 = -46.380396611 x = -46.380396611 Simplifying x = -46.380396611Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.380396611, -46.380396611}
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