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Simplifying x2 + 68x = 136 Reorder the terms: 68x + x2 = 136 Solving 68x + x2 = 136 Solving for variable 'x'. Reorder the terms: -136 + 68x + x2 = 136 + -136 Combine like terms: 136 + -136 = 0 -136 + 68x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '136' to each side of the equation. -136 + 68x + 136 + x2 = 0 + 136 Reorder the terms: -136 + 136 + 68x + x2 = 0 + 136 Combine like terms: -136 + 136 = 0 0 + 68x + x2 = 0 + 136 68x + x2 = 0 + 136 Combine like terms: 0 + 136 = 136 68x + x2 = 136 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 = 136 + 1156 Reorder the terms: 1156 + 68x + x2 = 136 + 1156 Combine like terms: 136 + 1156 = 1292 1156 + 68x + x2 = 1292 Factor a perfect square on the left side: (x + 34)(x + 34) = 1292 Calculate the square root of the right side: 35.944401511 Break this problem into two subproblems by setting (x + 34) equal to 35.944401511 and -35.944401511.Subproblem 1
x + 34 = 35.944401511 Simplifying x + 34 = 35.944401511 Reorder the terms: 34 + x = 35.944401511 Solving 34 + x = 35.944401511 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 = 35.944401511 + -34 Combine like terms: 34 + -34 = 0 0 + x = 35.944401511 + -34 x = 35.944401511 + -34 Combine like terms: 35.944401511 + -34 = 1.944401511 x = 1.944401511 Simplifying x = 1.944401511Subproblem 2
x + 34 = -35.944401511 Simplifying x + 34 = -35.944401511 Reorder the terms: 34 + x = -35.944401511 Solving 34 + x = -35.944401511 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 = -35.944401511 + -34 Combine like terms: 34 + -34 = 0 0 + x = -35.944401511 + -34 x = -35.944401511 + -34 Combine like terms: -35.944401511 + -34 = -69.944401511 x = -69.944401511 Simplifying x = -69.944401511Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.944401511, -69.944401511}
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