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Simplifying x2 + 68x + -45 = 0 Reorder the terms: -45 + 68x + x2 = 0 Solving -45 + 68x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '45' to each side of the equation. -45 + 68x + 45 + x2 = 0 + 45 Reorder the terms: -45 + 45 + 68x + x2 = 0 + 45 Combine like terms: -45 + 45 = 0 0 + 68x + x2 = 0 + 45 68x + x2 = 0 + 45 Combine like terms: 0 + 45 = 45 68x + x2 = 45 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 = 45 + 1156 Reorder the terms: 1156 + 68x + x2 = 45 + 1156 Combine like terms: 45 + 1156 = 1201 1156 + 68x + x2 = 1201 Factor a perfect square on the left side: (x + 34)(x + 34) = 1201 Calculate the square root of the right side: 34.655446902 Break this problem into two subproblems by setting (x + 34) equal to 34.655446902 and -34.655446902.Subproblem 1
x + 34 = 34.655446902 Simplifying x + 34 = 34.655446902 Reorder the terms: 34 + x = 34.655446902 Solving 34 + x = 34.655446902 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 = 34.655446902 + -34 Combine like terms: 34 + -34 = 0 0 + x = 34.655446902 + -34 x = 34.655446902 + -34 Combine like terms: 34.655446902 + -34 = 0.655446902 x = 0.655446902 Simplifying x = 0.655446902Subproblem 2
x + 34 = -34.655446902 Simplifying x + 34 = -34.655446902 Reorder the terms: 34 + x = -34.655446902 Solving 34 + x = -34.655446902 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 = -34.655446902 + -34 Combine like terms: 34 + -34 = 0 0 + x = -34.655446902 + -34 x = -34.655446902 + -34 Combine like terms: -34.655446902 + -34 = -68.655446902 x = -68.655446902 Simplifying x = -68.655446902Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.655446902, -68.655446902}
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