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Simplifying x2 + 68x = 68 Reorder the terms: 68x + x2 = 68 Solving 68x + x2 = 68 Solving for variable 'x'. Reorder the terms: -68 + 68x + x2 = 68 + -68 Combine like terms: 68 + -68 = 0 -68 + 68x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '68' to each side of the equation. -68 + 68x + 68 + x2 = 0 + 68 Reorder the terms: -68 + 68 + 68x + x2 = 0 + 68 Combine like terms: -68 + 68 = 0 0 + 68x + x2 = 0 + 68 68x + x2 = 0 + 68 Combine like terms: 0 + 68 = 68 68x + x2 = 68 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 = 68 + 1156 Reorder the terms: 1156 + 68x + x2 = 68 + 1156 Combine like terms: 68 + 1156 = 1224 1156 + 68x + x2 = 1224 Factor a perfect square on the left side: (x + 34)(x + 34) = 1224 Calculate the square root of the right side: 34.985711369 Break this problem into two subproblems by setting (x + 34) equal to 34.985711369 and -34.985711369.Subproblem 1
x + 34 = 34.985711369 Simplifying x + 34 = 34.985711369 Reorder the terms: 34 + x = 34.985711369 Solving 34 + x = 34.985711369 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 = 34.985711369 + -34 Combine like terms: 34 + -34 = 0 0 + x = 34.985711369 + -34 x = 34.985711369 + -34 Combine like terms: 34.985711369 + -34 = 0.985711369 x = 0.985711369 Simplifying x = 0.985711369Subproblem 2
x + 34 = -34.985711369 Simplifying x + 34 = -34.985711369 Reorder the terms: 34 + x = -34.985711369 Solving 34 + x = -34.985711369 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 = -34.985711369 + -34 Combine like terms: 34 + -34 = 0 0 + x = -34.985711369 + -34 x = -34.985711369 + -34 Combine like terms: -34.985711369 + -34 = -68.985711369 x = -68.985711369 Simplifying x = -68.985711369Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.985711369, -68.985711369}
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