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Simplifying x2 + 68x + 184 = 0 Reorder the terms: 184 + 68x + x2 = 0 Solving 184 + 68x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-184' to each side of the equation. 184 + 68x + -184 + x2 = 0 + -184 Reorder the terms: 184 + -184 + 68x + x2 = 0 + -184 Combine like terms: 184 + -184 = 0 0 + 68x + x2 = 0 + -184 68x + x2 = 0 + -184 Combine like terms: 0 + -184 = -184 68x + x2 = -184 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 = -184 + 1156 Reorder the terms: 1156 + 68x + x2 = -184 + 1156 Combine like terms: -184 + 1156 = 972 1156 + 68x + x2 = 972 Factor a perfect square on the left side: (x + 34)(x + 34) = 972 Calculate the square root of the right side: 31.176914536 Break this problem into two subproblems by setting (x + 34) equal to 31.176914536 and -31.176914536.Subproblem 1
x + 34 = 31.176914536 Simplifying x + 34 = 31.176914536 Reorder the terms: 34 + x = 31.176914536 Solving 34 + x = 31.176914536 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 = 31.176914536 + -34 Combine like terms: 34 + -34 = 0 0 + x = 31.176914536 + -34 x = 31.176914536 + -34 Combine like terms: 31.176914536 + -34 = -2.823085464 x = -2.823085464 Simplifying x = -2.823085464Subproblem 2
x + 34 = -31.176914536 Simplifying x + 34 = -31.176914536 Reorder the terms: 34 + x = -31.176914536 Solving 34 + x = -31.176914536 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 = -31.176914536 + -34 Combine like terms: 34 + -34 = 0 0 + x = -31.176914536 + -34 x = -31.176914536 + -34 Combine like terms: -31.176914536 + -34 = -65.176914536 x = -65.176914536 Simplifying x = -65.176914536Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.823085464, -65.176914536}
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