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Simplifying (x + -0.667)(x + 0.778) = 0 Reorder the terms: (-0.667 + x)(x + 0.778) = 0 Reorder the terms: (-0.667 + x)(0.778 + x) = 0 Multiply (-0.667 + x) * (0.778 + x) (-0.667(0.778 + x) + x(0.778 + x)) = 0 ((0.778 * -0.667 + x * -0.667) + x(0.778 + x)) = 0 ((-0.518926 + -0.667x) + x(0.778 + x)) = 0 (-0.518926 + -0.667x + (0.778 * x + x * x)) = 0 (-0.518926 + -0.667x + (0.778x + x2)) = 0 Combine like terms: -0.667x + 0.778x = 0.111x (-0.518926 + 0.111x + x2) = 0 Solving -0.518926 + 0.111x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '0.518926' to each side of the equation. -0.518926 + 0.111x + 0.518926 + x2 = 0 + 0.518926 Reorder the terms: -0.518926 + 0.518926 + 0.111x + x2 = 0 + 0.518926 Combine like terms: -0.518926 + 0.518926 = 0.000000 0.000000 + 0.111x + x2 = 0 + 0.518926 0.111x + x2 = 0 + 0.518926 Combine like terms: 0 + 0.518926 = 0.518926 0.111x + x2 = 0.518926 The x term is 0.111x. Take half its coefficient (0.0555). Square it (0.00308025) and add it to both sides. Add '0.00308025' to each side of the equation. 0.111x + 0.00308025 + x2 = 0.518926 + 0.00308025 Reorder the terms: 0.00308025 + 0.111x + x2 = 0.518926 + 0.00308025 Combine like terms: 0.518926 + 0.00308025 = 0.52200625 0.00308025 + 0.111x + x2 = 0.52200625 Factor a perfect square on the left side: (x + 0.0555)(x + 0.0555) = 0.52200625 Calculate the square root of the right side: 0.7225 Break this problem into two subproblems by setting (x + 0.0555) equal to 0.7225 and -0.7225.Subproblem 1
x + 0.0555 = 0.7225 Simplifying x + 0.0555 = 0.7225 Reorder the terms: 0.0555 + x = 0.7225 Solving 0.0555 + x = 0.7225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0555' to each side of the equation. 0.0555 + -0.0555 + x = 0.7225 + -0.0555 Combine like terms: 0.0555 + -0.0555 = 0.0000 0.0000 + x = 0.7225 + -0.0555 x = 0.7225 + -0.0555 Combine like terms: 0.7225 + -0.0555 = 0.667 x = 0.667 Simplifying x = 0.667Subproblem 2
x + 0.0555 = -0.7225 Simplifying x + 0.0555 = -0.7225 Reorder the terms: 0.0555 + x = -0.7225 Solving 0.0555 + x = -0.7225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0555' to each side of the equation. 0.0555 + -0.0555 + x = -0.7225 + -0.0555 Combine like terms: 0.0555 + -0.0555 = 0.0000 0.0000 + x = -0.7225 + -0.0555 x = -0.7225 + -0.0555 Combine like terms: -0.7225 + -0.0555 = -0.778 x = -0.778 Simplifying x = -0.778Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.667, -0.778}
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