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Simplifying x2 + -34x = 750 Reorder the terms: -34x + x2 = 750 Solving -34x + x2 = 750 Solving for variable 'x'. Reorder the terms: -750 + -34x + x2 = 750 + -750 Combine like terms: 750 + -750 = 0 -750 + -34x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '750' to each side of the equation. -750 + -34x + 750 + x2 = 0 + 750 Reorder the terms: -750 + 750 + -34x + x2 = 0 + 750 Combine like terms: -750 + 750 = 0 0 + -34x + x2 = 0 + 750 -34x + x2 = 0 + 750 Combine like terms: 0 + 750 = 750 -34x + x2 = 750 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 = 750 + 289 Reorder the terms: 289 + -34x + x2 = 750 + 289 Combine like terms: 750 + 289 = 1039 289 + -34x + x2 = 1039 Factor a perfect square on the left side: (x + -17)(x + -17) = 1039 Calculate the square root of the right side: 32.233522923 Break this problem into two subproblems by setting (x + -17) equal to 32.233522923 and -32.233522923.Subproblem 1
x + -17 = 32.233522923 Simplifying x + -17 = 32.233522923 Reorder the terms: -17 + x = 32.233522923 Solving -17 + x = 32.233522923 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 = 32.233522923 + 17 Combine like terms: -17 + 17 = 0 0 + x = 32.233522923 + 17 x = 32.233522923 + 17 Combine like terms: 32.233522923 + 17 = 49.233522923 x = 49.233522923 Simplifying x = 49.233522923Subproblem 2
x + -17 = -32.233522923 Simplifying x + -17 = -32.233522923 Reorder the terms: -17 + x = -32.233522923 Solving -17 + x = -32.233522923 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 = -32.233522923 + 17 Combine like terms: -17 + 17 = 0 0 + x = -32.233522923 + 17 x = -32.233522923 + 17 Combine like terms: -32.233522923 + 17 = -15.233522923 x = -15.233522923 Simplifying x = -15.233522923Solution
The solution to the problem is based on the solutions from the subproblems. x = {49.233522923, -15.233522923}
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