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Simplifying 0.222x2 + -1.11x + 0.889 = 0 Reorder the terms: 0.889 + -1.11x + 0.222x2 = 0 Solving 0.889 + -1.11x + 0.222x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.222 the coefficient of the squared term: Divide each side by '0.222'. 4.004504505 + -5x + x2 = 0 Move the constant term to the right: Add '-4.004504505' to each side of the equation. 4.004504505 + -5x + -4.004504505 + x2 = 0 + -4.004504505 Reorder the terms: 4.004504505 + -4.004504505 + -5x + x2 = 0 + -4.004504505 Combine like terms: 4.004504505 + -4.004504505 = 0.000000000 0.000000000 + -5x + x2 = 0 + -4.004504505 -5x + x2 = 0 + -4.004504505 Combine like terms: 0 + -4.004504505 = -4.004504505 -5x + x2 = -4.004504505 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -4.004504505 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -4.004504505 + 6.25 Combine like terms: -4.004504505 + 6.25 = 2.245495495 6.25 + -5x + x2 = 2.245495495 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 2.245495495 Calculate the square root of the right side: 1.498497746 Break this problem into two subproblems by setting (x + -2.5) equal to 1.498497746 and -1.498497746.Subproblem 1
x + -2.5 = 1.498497746 Simplifying x + -2.5 = 1.498497746 Reorder the terms: -2.5 + x = 1.498497746 Solving -2.5 + x = 1.498497746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.498497746 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.498497746 + 2.5 x = 1.498497746 + 2.5 Combine like terms: 1.498497746 + 2.5 = 3.998497746 x = 3.998497746 Simplifying x = 3.998497746Subproblem 2
x + -2.5 = -1.498497746 Simplifying x + -2.5 = -1.498497746 Reorder the terms: -2.5 + x = -1.498497746 Solving -2.5 + x = -1.498497746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.498497746 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.498497746 + 2.5 x = -1.498497746 + 2.5 Combine like terms: -1.498497746 + 2.5 = 1.001502254 x = 1.001502254 Simplifying x = 1.001502254Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.998497746, 1.001502254}
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