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Simplifying x2 + -1.11x + 0.30 = 0.50 Reorder the terms: 0.30 + -1.11x + x2 = 0.50 Solving 0.30 + -1.11x + x2 = 0.50 Solving for variable 'x'. Reorder the terms: 0.30 + -0.50 + -1.11x + x2 = 0.50 + -0.50 Combine like terms: 0.30 + -0.50 = -0.2 -0.2 + -1.11x + x2 = 0.50 + -0.50 Combine like terms: 0.50 + -0.50 = 0.00 -0.2 + -1.11x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -1.11x + 0.2 + x2 = 0.00 + 0.2 Reorder the terms: -0.2 + 0.2 + -1.11x + x2 = 0.00 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -1.11x + x2 = 0.00 + 0.2 -1.11x + x2 = 0.00 + 0.2 Combine like terms: 0.00 + 0.2 = 0.2 -1.11x + x2 = 0.2 The x term is -1.11x. Take half its coefficient (-0.555). Square it (0.308025) and add it to both sides. Add '0.308025' to each side of the equation. -1.11x + 0.308025 + x2 = 0.2 + 0.308025 Reorder the terms: 0.308025 + -1.11x + x2 = 0.2 + 0.308025 Combine like terms: 0.2 + 0.308025 = 0.508025 0.308025 + -1.11x + x2 = 0.508025 Factor a perfect square on the left side: (x + -0.555)(x + -0.555) = 0.508025 Calculate the square root of the right side: 0.712758725 Break this problem into two subproblems by setting (x + -0.555) equal to 0.712758725 and -0.712758725.Subproblem 1
x + -0.555 = 0.712758725 Simplifying x + -0.555 = 0.712758725 Reorder the terms: -0.555 + x = 0.712758725 Solving -0.555 + x = 0.712758725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.555' to each side of the equation. -0.555 + 0.555 + x = 0.712758725 + 0.555 Combine like terms: -0.555 + 0.555 = 0.000 0.000 + x = 0.712758725 + 0.555 x = 0.712758725 + 0.555 Combine like terms: 0.712758725 + 0.555 = 1.267758725 x = 1.267758725 Simplifying x = 1.267758725Subproblem 2
x + -0.555 = -0.712758725 Simplifying x + -0.555 = -0.712758725 Reorder the terms: -0.555 + x = -0.712758725 Solving -0.555 + x = -0.712758725 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.555' to each side of the equation. -0.555 + 0.555 + x = -0.712758725 + 0.555 Combine like terms: -0.555 + 0.555 = 0.000 0.000 + x = -0.712758725 + 0.555 x = -0.712758725 + 0.555 Combine like terms: -0.712758725 + 0.555 = -0.157758725 x = -0.157758725 Simplifying x = -0.157758725Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.267758725, -0.157758725}
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