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Simplifying 2x2 + -12x + -36 = (x + 2) Reorder the terms: -36 + -12x + 2x2 = (x + 2) Reorder the terms: -36 + -12x + 2x2 = (2 + x) Remove parenthesis around (2 + x) -36 + -12x + 2x2 = 2 + x Solving -36 + -12x + 2x2 = 2 + x Solving for variable 'x'. Reorder the terms: -36 + -2 + -12x + -1x + 2x2 = 2 + x + -2 + -1x Combine like terms: -36 + -2 = -38 -38 + -12x + -1x + 2x2 = 2 + x + -2 + -1x Combine like terms: -12x + -1x = -13x -38 + -13x + 2x2 = 2 + x + -2 + -1x Reorder the terms: -38 + -13x + 2x2 = 2 + -2 + x + -1x Combine like terms: 2 + -2 = 0 -38 + -13x + 2x2 = 0 + x + -1x -38 + -13x + 2x2 = x + -1x Combine like terms: x + -1x = 0 -38 + -13x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -19 + -6.5x + x2 = 0 Move the constant term to the right: Add '19' to each side of the equation. -19 + -6.5x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -6.5x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -6.5x + x2 = 0 + 19 -6.5x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -6.5x + x2 = 19 The x term is -6.5x. Take half its coefficient (-3.25). Square it (10.5625) and add it to both sides. Add '10.5625' to each side of the equation. -6.5x + 10.5625 + x2 = 19 + 10.5625 Reorder the terms: 10.5625 + -6.5x + x2 = 19 + 10.5625 Combine like terms: 19 + 10.5625 = 29.5625 10.5625 + -6.5x + x2 = 29.5625 Factor a perfect square on the left side: (x + -3.25)(x + -3.25) = 29.5625 Calculate the square root of the right side: 5.437140793 Break this problem into two subproblems by setting (x + -3.25) equal to 5.437140793 and -5.437140793.Subproblem 1
x + -3.25 = 5.437140793 Simplifying x + -3.25 = 5.437140793 Reorder the terms: -3.25 + x = 5.437140793 Solving -3.25 + x = 5.437140793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = 5.437140793 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = 5.437140793 + 3.25 x = 5.437140793 + 3.25 Combine like terms: 5.437140793 + 3.25 = 8.687140793 x = 8.687140793 Simplifying x = 8.687140793Subproblem 2
x + -3.25 = -5.437140793 Simplifying x + -3.25 = -5.437140793 Reorder the terms: -3.25 + x = -5.437140793 Solving -3.25 + x = -5.437140793 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.25' to each side of the equation. -3.25 + 3.25 + x = -5.437140793 + 3.25 Combine like terms: -3.25 + 3.25 = 0.00 0.00 + x = -5.437140793 + 3.25 x = -5.437140793 + 3.25 Combine like terms: -5.437140793 + 3.25 = -2.187140793 x = -2.187140793 Simplifying x = -2.187140793Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.687140793, -2.187140793}
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