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Simplifying x2 + -13x + -34 = 0 Reorder the terms: -34 + -13x + x2 = 0 Solving -34 + -13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '34' to each side of the equation. -34 + -13x + 34 + x2 = 0 + 34 Reorder the terms: -34 + 34 + -13x + x2 = 0 + 34 Combine like terms: -34 + 34 = 0 0 + -13x + x2 = 0 + 34 -13x + x2 = 0 + 34 Combine like terms: 0 + 34 = 34 -13x + x2 = 34 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 = 34 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 34 + 42.25 Combine like terms: 34 + 42.25 = 76.25 42.25 + -13x + x2 = 76.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 76.25 Calculate the square root of the right side: 8.732124598 Break this problem into two subproblems by setting (x + -6.5) equal to 8.732124598 and -8.732124598.Subproblem 1
x + -6.5 = 8.732124598 Simplifying x + -6.5 = 8.732124598 Reorder the terms: -6.5 + x = 8.732124598 Solving -6.5 + x = 8.732124598 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 = 8.732124598 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 8.732124598 + 6.5 x = 8.732124598 + 6.5 Combine like terms: 8.732124598 + 6.5 = 15.232124598 x = 15.232124598 Simplifying x = 15.232124598Subproblem 2
x + -6.5 = -8.732124598 Simplifying x + -6.5 = -8.732124598 Reorder the terms: -6.5 + x = -8.732124598 Solving -6.5 + x = -8.732124598 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 = -8.732124598 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -8.732124598 + 6.5 x = -8.732124598 + 6.5 Combine like terms: -8.732124598 + 6.5 = -2.232124598 x = -2.232124598 Simplifying x = -2.232124598Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.232124598, -2.232124598}
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