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Simplifying x2 + 68x = 1156 Reorder the terms: 68x + x2 = 1156 Solving 68x + x2 = 1156 Solving for variable 'x'. Reorder the terms: -1156 + 68x + x2 = 1156 + -1156 Combine like terms: 1156 + -1156 = 0 -1156 + 68x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1156' to each side of the equation. -1156 + 68x + 1156 + x2 = 0 + 1156 Reorder the terms: -1156 + 1156 + 68x + x2 = 0 + 1156 Combine like terms: -1156 + 1156 = 0 0 + 68x + x2 = 0 + 1156 68x + x2 = 0 + 1156 Combine like terms: 0 + 1156 = 1156 68x + x2 = 1156 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 = 1156 + 1156 Reorder the terms: 1156 + 68x + x2 = 1156 + 1156 Combine like terms: 1156 + 1156 = 2312 1156 + 68x + x2 = 2312 Factor a perfect square on the left side: (x + 34)(x + 34) = 2312 Calculate the square root of the right side: 48.083261121 Break this problem into two subproblems by setting (x + 34) equal to 48.083261121 and -48.083261121.Subproblem 1
x + 34 = 48.083261121 Simplifying x + 34 = 48.083261121 Reorder the terms: 34 + x = 48.083261121 Solving 34 + x = 48.083261121 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 = 48.083261121 + -34 Combine like terms: 34 + -34 = 0 0 + x = 48.083261121 + -34 x = 48.083261121 + -34 Combine like terms: 48.083261121 + -34 = 14.083261121 x = 14.083261121 Simplifying x = 14.083261121Subproblem 2
x + 34 = -48.083261121 Simplifying x + 34 = -48.083261121 Reorder the terms: 34 + x = -48.083261121 Solving 34 + x = -48.083261121 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 = -48.083261121 + -34 Combine like terms: 34 + -34 = 0 0 + x = -48.083261121 + -34 x = -48.083261121 + -34 Combine like terms: -48.083261121 + -34 = -82.083261121 x = -82.083261121 Simplifying x = -82.083261121Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.083261121, -82.083261121}
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