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Simplifying x2 + -13x + -72 = 0 Reorder the terms: -72 + -13x + x2 = 0 Solving -72 + -13x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -13x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + -13x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -13x + x2 = 0 + 72 -13x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 -13x + x2 = 72 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 = 72 + 42.25 Reorder the terms: 42.25 + -13x + x2 = 72 + 42.25 Combine like terms: 72 + 42.25 = 114.25 42.25 + -13x + x2 = 114.25 Factor a perfect square on the left side: (x + -6.5)(x + -6.5) = 114.25 Calculate the square root of the right side: 10.688779163 Break this problem into two subproblems by setting (x + -6.5) equal to 10.688779163 and -10.688779163.Subproblem 1
x + -6.5 = 10.688779163 Simplifying x + -6.5 = 10.688779163 Reorder the terms: -6.5 + x = 10.688779163 Solving -6.5 + x = 10.688779163 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 = 10.688779163 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = 10.688779163 + 6.5 x = 10.688779163 + 6.5 Combine like terms: 10.688779163 + 6.5 = 17.188779163 x = 17.188779163 Simplifying x = 17.188779163Subproblem 2
x + -6.5 = -10.688779163 Simplifying x + -6.5 = -10.688779163 Reorder the terms: -6.5 + x = -10.688779163 Solving -6.5 + x = -10.688779163 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 = -10.688779163 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + x = -10.688779163 + 6.5 x = -10.688779163 + 6.5 Combine like terms: -10.688779163 + 6.5 = -4.188779163 x = -4.188779163 Simplifying x = -4.188779163Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.188779163, -4.188779163}
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