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Simplifying x2 + 68x + -170 = 0 Reorder the terms: -170 + 68x + x2 = 0 Solving -170 + 68x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '170' to each side of the equation. -170 + 68x + 170 + x2 = 0 + 170 Reorder the terms: -170 + 170 + 68x + x2 = 0 + 170 Combine like terms: -170 + 170 = 0 0 + 68x + x2 = 0 + 170 68x + x2 = 0 + 170 Combine like terms: 0 + 170 = 170 68x + x2 = 170 The x term is 68x. Take half its coefficient (34). Square it (1156) and add it to both sides. Add '1156' to each side of the equation. 68x + 1156 + x2 = 170 + 1156 Reorder the terms: 1156 + 68x + x2 = 170 + 1156 Combine like terms: 170 + 1156 = 1326 1156 + 68x + x2 = 1326 Factor a perfect square on the left side: (x + 34)(x + 34) = 1326 Calculate the square root of the right side: 36.414282912 Break this problem into two subproblems by setting (x + 34) equal to 36.414282912 and -36.414282912.Subproblem 1
x + 34 = 36.414282912 Simplifying x + 34 = 36.414282912 Reorder the terms: 34 + x = 36.414282912 Solving 34 + x = 36.414282912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34' to each side of the equation. 34 + -34 + x = 36.414282912 + -34 Combine like terms: 34 + -34 = 0 0 + x = 36.414282912 + -34 x = 36.414282912 + -34 Combine like terms: 36.414282912 + -34 = 2.414282912 x = 2.414282912 Simplifying x = 2.414282912Subproblem 2
x + 34 = -36.414282912 Simplifying x + 34 = -36.414282912 Reorder the terms: 34 + x = -36.414282912 Solving 34 + x = -36.414282912 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-34' to each side of the equation. 34 + -34 + x = -36.414282912 + -34 Combine like terms: 34 + -34 = 0 0 + x = -36.414282912 + -34 x = -36.414282912 + -34 Combine like terms: -36.414282912 + -34 = -70.414282912 x = -70.414282912 Simplifying x = -70.414282912Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.414282912, -70.414282912}
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