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Simplifying x2 + -13x = 60 Reorder the terms: -13x + x2 = 60 Solving -13x + x2 = 60 Solving for variable 'x'. Reorder the terms: -60 + -13x + x2 = 60 + -60 Combine like terms: 60 + -60 = 0 -60 + -13x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + -13x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + -13x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + -13x + x2 = 0 + 60 -13x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 -13x + x2 = 60 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 = 60 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 60 + 42.25 Combine like terms: 60 + 42.25 = 102.25 42.25 + -13x + x2 = 102.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 102.25 Calculate the square root of the right side: 10.111874208 Break this problem into two subproblems by setting (x + -6.5) equal to 10.111874208 and -10.111874208.Subproblem 1
x + -6.5 = 10.111874208 Simplifying x + -6.5 = 10.111874208 Reorder the terms: -6.5 + x = 10.111874208 Solving -6.5 + x = 10.111874208 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 = 10.111874208 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 10.111874208 + 6.5 x = 10.111874208 + 6.5 Combine like terms: 10.111874208 + 6.5 = 16.611874208 x = 16.611874208 Simplifying x = 16.611874208Subproblem 2
x + -6.5 = -10.111874208 Simplifying x + -6.5 = -10.111874208 Reorder the terms: -6.5 + x = -10.111874208 Solving -6.5 + x = -10.111874208 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 = -10.111874208 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -10.111874208 + 6.5 x = -10.111874208 + 6.5 Combine like terms: -10.111874208 + 6.5 = -3.611874208 x = -3.611874208 Simplifying x = -3.611874208Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.611874208, -3.611874208}
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