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Simplifying x2 + -66x + 224 = 0 Reorder the terms: 224 + -66x + x2 = 0 Solving 224 + -66x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-224' to each side of the equation. 224 + -66x + -224 + x2 = 0 + -224 Reorder the terms: 224 + -224 + -66x + x2 = 0 + -224 Combine like terms: 224 + -224 = 0 0 + -66x + x2 = 0 + -224 -66x + x2 = 0 + -224 Combine like terms: 0 + -224 = -224 -66x + x2 = -224 The x term is -66x. Take half its coefficient (-33). Square it (1089) and add it to both sides. Add '1089' to each side of the equation. -66x + 1089 + x2 = -224 + 1089 Reorder the terms: 1089 + -66x + x2 = -224 + 1089 Combine like terms: -224 + 1089 = 865 1089 + -66x + x2 = 865 Factor a perfect square on the left side: (x + -33)(x + -33) = 865 Calculate the square root of the right side: 29.41088234 Break this problem into two subproblems by setting (x + -33) equal to 29.41088234 and -29.41088234.Subproblem 1
x + -33 = 29.41088234 Simplifying x + -33 = 29.41088234 Reorder the terms: -33 + x = 29.41088234 Solving -33 + x = 29.41088234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 33 + x = 29.41088234 + 33 Combine like terms: -33 + 33 = 0 0 + x = 29.41088234 + 33 x = 29.41088234 + 33 Combine like terms: 29.41088234 + 33 = 62.41088234 x = 62.41088234 Simplifying x = 62.41088234Subproblem 2
x + -33 = -29.41088234 Simplifying x + -33 = -29.41088234 Reorder the terms: -33 + x = -29.41088234 Solving -33 + x = -29.41088234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '33' to each side of the equation. -33 + 33 + x = -29.41088234 + 33 Combine like terms: -33 + 33 = 0 0 + x = -29.41088234 + 33 x = -29.41088234 + 33 Combine like terms: -29.41088234 + 33 = 3.58911766 x = 3.58911766 Simplifying x = 3.58911766Solution
The solution to the problem is based on the solutions from the subproblems. x = {62.41088234, 3.58911766}
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