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Simplifying 2x2 + 13x + 34 = x2 + 36 Reorder the terms: 34 + 13x + 2x2 = x2 + 36 Reorder the terms: 34 + 13x + 2x2 = 36 + x2 Solving 34 + 13x + 2x2 = 36 + x2 Solving for variable 'x'. Reorder the terms: 34 + -36 + 13x + 2x2 + -1x2 = 36 + x2 + -36 + -1x2 Combine like terms: 34 + -36 = -2 -2 + 13x + 2x2 + -1x2 = 36 + x2 + -36 + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -2 + 13x + 1x2 = 36 + x2 + -36 + -1x2 Reorder the terms: -2 + 13x + 1x2 = 36 + -36 + x2 + -1x2 Combine like terms: 36 + -36 = 0 -2 + 13x + 1x2 = 0 + x2 + -1x2 -2 + 13x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -2 + 13x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 13x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 13x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 13x + x2 = 0 + 2 13x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 13x + x2 = 2 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 = 2 + 42.25 Reorder the terms: 42.25 + 13x + x2 = 2 + 42.25 Combine like terms: 2 + 42.25 = 44.25 42.25 + 13x + x2 = 44.25 Factor a perfect square on the left side: (x + 6.5)(x + 6.5) = 44.25 Calculate the square root of the right side: 6.652067348 Break this problem into two subproblems by setting (x + 6.5) equal to 6.652067348 and -6.652067348.Subproblem 1
x + 6.5 = 6.652067348 Simplifying x + 6.5 = 6.652067348 Reorder the terms: 6.5 + x = 6.652067348 Solving 6.5 + x = 6.652067348 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 = 6.652067348 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = 6.652067348 + -6.5 x = 6.652067348 + -6.5 Combine like terms: 6.652067348 + -6.5 = 0.152067348 x = 0.152067348 Simplifying x = 0.152067348Subproblem 2
x + 6.5 = -6.652067348 Simplifying x + 6.5 = -6.652067348 Reorder the terms: 6.5 + x = -6.652067348 Solving 6.5 + x = -6.652067348 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 = -6.652067348 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + x = -6.652067348 + -6.5 x = -6.652067348 + -6.5 Combine like terms: -6.652067348 + -6.5 = -13.152067348 x = -13.152067348 Simplifying x = -13.152067348Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.152067348, -13.152067348}
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