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Simplifying x2 + 13x + 12 = -23 Reorder the terms: 12 + 13x + x2 = -23 Solving 12 + 13x + x2 = -23 Solving for variable 'x'. Reorder the terms: 12 + 23 + 13x + x2 = -23 + 23 Combine like terms: 12 + 23 = 35 35 + 13x + x2 = -23 + 23 Combine like terms: -23 + 23 = 0 35 + 13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-35' to each side of the equation. 35 + 13x + -35 + x2 = 0 + -35 Reorder the terms: 35 + -35 + 13x + x2 = 0 + -35 Combine like terms: 35 + -35 = 0 0 + 13x + x2 = 0 + -35 13x + x2 = 0 + -35 Combine like terms: 0 + -35 = -35 13x + x2 = -35 The x term is 13x. Take half its coefficient (6.5). Square it (42.25) and add it to both sides. Add '42.25' to each side of the equation. 13x + 42.25 + x2 = -35 + 42.25 Reorder the terms: 42.25 + 13x + x2 = -35 + 42.25 Combine like terms: -35 + 42.25 = 7.25 42.25 + 13x + x2 = 7.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 7.25 Calculate the square root of the right side: 2.692582404 Break this problem into two subproblems by setting (x + 6.5) equal to 2.692582404 and -2.692582404.Subproblem 1
x + 6.5 = 2.692582404 Simplifying x + 6.5 = 2.692582404 Reorder the terms: 6.5 + x = 2.692582404 Solving 6.5 + x = 2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = 2.692582404 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 2.692582404 + -6.5 x = 2.692582404 + -6.5 Combine like terms: 2.692582404 + -6.5 = -3.807417596 x = -3.807417596 Simplifying x = -3.807417596Subproblem 2
x + 6.5 = -2.692582404 Simplifying x + 6.5 = -2.692582404 Reorder the terms: 6.5 + x = -2.692582404 Solving 6.5 + x = -2.692582404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + x = -2.692582404 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -2.692582404 + -6.5 x = -2.692582404 + -6.5 Combine like terms: -2.692582404 + -6.5 = -9.192582404 x = -9.192582404 Simplifying x = -9.192582404Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.807417596, -9.192582404}
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