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Simplifying -4x2 + x + 0.25 = 0 Reorder the terms: 0.25 + x + -4x2 = 0 Solving 0.25 + x + -4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -0.0625 + -0.25x + x2 = 0 Move the constant term to the right: Add '0.0625' to each side of the equation. -0.0625 + -0.25x + 0.0625 + x2 = 0 + 0.0625 Reorder the terms: -0.0625 + 0.0625 + -0.25x + x2 = 0 + 0.0625 Combine like terms: -0.0625 + 0.0625 = 0.0000 0.0000 + -0.25x + x2 = 0 + 0.0625 -0.25x + x2 = 0 + 0.0625 Combine like terms: 0 + 0.0625 = 0.0625 -0.25x + x2 = 0.0625 The x term is x. 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. -0.25x + 0.25 + x2 = 0.0625 + 0.25 Reorder the terms: 0.25 + -0.25x + x2 = 0.0625 + 0.25 Combine like terms: 0.0625 + 0.25 = 0.3125 0.25 + -0.25x + x2 = 0.3125 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 0.3125 Calculate the square root of the right side: 0.559016994 Break this problem into two subproblems by setting (x + 0.5) equal to 0.559016994 and -0.559016994.Subproblem 1
x + 0.5 = 0.559016994 Simplifying x + 0.5 = 0.559016994 Reorder the terms: 0.5 + x = 0.559016994 Solving 0.5 + x = 0.559016994 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 = 0.559016994 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 0.559016994 + -0.5 x = 0.559016994 + -0.5 Combine like terms: 0.559016994 + -0.5 = 0.059016994 x = 0.059016994 Simplifying x = 0.059016994Subproblem 2
x + 0.5 = -0.559016994 Simplifying x + 0.5 = -0.559016994 Reorder the terms: 0.5 + x = -0.559016994 Solving 0.5 + x = -0.559016994 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 = -0.559016994 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -0.559016994 + -0.5 x = -0.559016994 + -0.5 Combine like terms: -0.559016994 + -0.5 = -1.059016994 x = -1.059016994 Simplifying x = -1.059016994Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.059016994, -1.059016994}
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