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Simplifying 0 = 5.8x2 + -5.8x + 1 Reorder the terms: 0 = 1 + -5.8x + 5.8x2 Solving 0 = 1 + -5.8x + 5.8x2 Solving for variable 'x'. Combine like terms: 0 + -1 = -1 -1 + 5.8x + -5.8x2 = 1 + -5.8x + 5.8x2 + -1 + 5.8x + -5.8x2 Reorder the terms: -1 + 5.8x + -5.8x2 = 1 + -1 + -5.8x + 5.8x + 5.8x2 + -5.8x2 Combine like terms: 1 + -1 = 0 -1 + 5.8x + -5.8x2 = 0 + -5.8x + 5.8x + 5.8x2 + -5.8x2 -1 + 5.8x + -5.8x2 = -5.8x + 5.8x + 5.8x2 + -5.8x2 Combine like terms: -5.8x + 5.8x = 0.0 -1 + 5.8x + -5.8x2 = 0.0 + 5.8x2 + -5.8x2 -1 + 5.8x + -5.8x2 = 5.8x2 + -5.8x2 Combine like terms: 5.8x2 + -5.8x2 = 0.0 -1 + 5.8x + -5.8x2 = 0.0 Begin completing the square. Divide all terms by -5.8 the coefficient of the squared term: Divide each side by '-5.8'. 0.1724137931 + -1x + x2 = 0 Move the constant term to the right: Add '-0.1724137931' to each side of the equation. 0.1724137931 + -1x + -0.1724137931 + x2 = 0 + -0.1724137931 Reorder the terms: 0.1724137931 + -0.1724137931 + -1x + x2 = 0 + -0.1724137931 Combine like terms: 0.1724137931 + -0.1724137931 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + -0.1724137931 -1x + x2 = 0 + -0.1724137931 Combine like terms: 0 + -0.1724137931 = -0.1724137931 -1x + x2 = -0.1724137931 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = -0.1724137931 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.1724137931 + 0.25 Combine like terms: -0.1724137931 + 0.25 = 0.0775862069 0.25 + -1x + x2 = 0.0775862069 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.0775862069 Calculate the square root of the right side: 0.278543007 Break this problem into two subproblems by setting (x + -0.5) equal to 0.278543007 and -0.278543007.Subproblem 1
x + -0.5 = 0.278543007 Simplifying x + -0.5 = 0.278543007 Reorder the terms: -0.5 + x = 0.278543007 Solving -0.5 + x = 0.278543007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.278543007 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.278543007 + 0.5 x = 0.278543007 + 0.5 Combine like terms: 0.278543007 + 0.5 = 0.778543007 x = 0.778543007 Simplifying x = 0.778543007Subproblem 2
x + -0.5 = -0.278543007 Simplifying x + -0.5 = -0.278543007 Reorder the terms: -0.5 + x = -0.278543007 Solving -0.5 + x = -0.278543007 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.278543007 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.278543007 + 0.5 x = -0.278543007 + 0.5 Combine like terms: -0.278543007 + 0.5 = 0.221456993 x = 0.221456993 Simplifying x = 0.221456993Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.778543007, 0.221456993}
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