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Simplifying x2 + -34x + 100 = 0 Reorder the terms: 100 + -34x + x2 = 0 Solving 100 + -34x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-100' to each side of the equation. 100 + -34x + -100 + x2 = 0 + -100 Reorder the terms: 100 + -100 + -34x + x2 = 0 + -100 Combine like terms: 100 + -100 = 0 0 + -34x + x2 = 0 + -100 -34x + x2 = 0 + -100 Combine like terms: 0 + -100 = -100 -34x + x2 = -100 The x term is -34x. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34x + 289 + x2 = -100 + 289 Reorder the terms: 289 + -34x + x2 = -100 + 289 Combine like terms: -100 + 289 = 189 289 + -34x + x2 = 189 Factor a perfect square on the left side: (x + -17)(x + -17) = 189 Calculate the square root of the right side: 13.747727085 Break this problem into two subproblems by setting (x + -17) equal to 13.747727085 and -13.747727085.Subproblem 1
x + -17 = 13.747727085 Simplifying x + -17 = 13.747727085 Reorder the terms: -17 + x = 13.747727085 Solving -17 + x = 13.747727085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 13.747727085 + 17 Combine like terms: -17 + 17 = 0 0 + x = 13.747727085 + 17 x = 13.747727085 + 17 Combine like terms: 13.747727085 + 17 = 30.747727085 x = 30.747727085 Simplifying x = 30.747727085Subproblem 2
x + -17 = -13.747727085 Simplifying x + -17 = -13.747727085 Reorder the terms: -17 + x = -13.747727085 Solving -17 + x = -13.747727085 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = -13.747727085 + 17 Combine like terms: -17 + 17 = 0 0 + x = -13.747727085 + 17 x = -13.747727085 + 17 Combine like terms: -13.747727085 + 17 = 3.252272915 x = 3.252272915 Simplifying x = 3.252272915Solution
The solution to the problem is based on the solutions from the subproblems. x = {30.747727085, 3.252272915}
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