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Simplifying x2 + 108x + -405 = 0 Reorder the terms: -405 + 108x + x2 = 0 Solving -405 + 108x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '405' to each side of the equation. -405 + 108x + 405 + x2 = 0 + 405 Reorder the terms: -405 + 405 + 108x + x2 = 0 + 405 Combine like terms: -405 + 405 = 0 0 + 108x + x2 = 0 + 405 108x + x2 = 0 + 405 Combine like terms: 0 + 405 = 405 108x + x2 = 405 The x term is 108x. Take half its coefficient (54). Square it (2916) and add it to both sides. Add '2916' to each side of the equation. 108x + 2916 + x2 = 405 + 2916 Reorder the terms: 2916 + 108x + x2 = 405 + 2916 Combine like terms: 405 + 2916 = 3321 2916 + 108x + x2 = 3321 Factor a perfect square on the left side: (x + 54)(x + 54) = 3321 Calculate the square root of the right side: 57.628118137 Break this problem into two subproblems by setting (x + 54) equal to 57.628118137 and -57.628118137.Subproblem 1
x + 54 = 57.628118137 Simplifying x + 54 = 57.628118137 Reorder the terms: 54 + x = 57.628118137 Solving 54 + x = 57.628118137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-54' to each side of the equation. 54 + -54 + x = 57.628118137 + -54 Combine like terms: 54 + -54 = 0 0 + x = 57.628118137 + -54 x = 57.628118137 + -54 Combine like terms: 57.628118137 + -54 = 3.628118137 x = 3.628118137 Simplifying x = 3.628118137Subproblem 2
x + 54 = -57.628118137 Simplifying x + 54 = -57.628118137 Reorder the terms: 54 + x = -57.628118137 Solving 54 + x = -57.628118137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-54' to each side of the equation. 54 + -54 + x = -57.628118137 + -54 Combine like terms: 54 + -54 = 0 0 + x = -57.628118137 + -54 x = -57.628118137 + -54 Combine like terms: -57.628118137 + -54 = -111.628118137 x = -111.628118137 Simplifying x = -111.628118137Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.628118137, -111.628118137}
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