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Simplifying 0 = 2x2 + -8x + 0.25 Reorder the terms: 0 = 0.25 + -8x + 2x2 Solving 0 = 0.25 + -8x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -0.25 = -0.25 -0.25 + 8x + -2x2 = 0.25 + -8x + 2x2 + -0.25 + 8x + -2x2 Reorder the terms: -0.25 + 8x + -2x2 = 0.25 + -0.25 + -8x + 8x + 2x2 + -2x2 Combine like terms: 0.25 + -0.25 = 0.00 -0.25 + 8x + -2x2 = 0.00 + -8x + 8x + 2x2 + -2x2 -0.25 + 8x + -2x2 = -8x + 8x + 2x2 + -2x2 Combine like terms: -8x + 8x = 0 -0.25 + 8x + -2x2 = 0 + 2x2 + -2x2 -0.25 + 8x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -0.25 + 8x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 0.125 + -4x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -4x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -4x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -4x + x2 = 0 + -0.125 -4x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -4x + x2 = -0.125 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -0.125 + 4 Reorder the terms: 4 + -4x + x2 = -0.125 + 4 Combine like terms: -0.125 + 4 = 3.875 4 + -4x + x2 = 3.875 Factor a perfect square on the left side: (x + -2)(x + -2) = 3.875 Calculate the square root of the right side: 1.968501969 Break this problem into two subproblems by setting (x + -2) equal to 1.968501969 and -1.968501969.Subproblem 1
x + -2 = 1.968501969 Simplifying x + -2 = 1.968501969 Reorder the terms: -2 + x = 1.968501969 Solving -2 + x = 1.968501969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.968501969 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.968501969 + 2 x = 1.968501969 + 2 Combine like terms: 1.968501969 + 2 = 3.968501969 x = 3.968501969 Simplifying x = 3.968501969Subproblem 2
x + -2 = -1.968501969 Simplifying x + -2 = -1.968501969 Reorder the terms: -2 + x = -1.968501969 Solving -2 + x = -1.968501969 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.968501969 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.968501969 + 2 x = -1.968501969 + 2 Combine like terms: -1.968501969 + 2 = 0.031498031 x = 0.031498031 Simplifying x = 0.031498031Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.968501969, 0.031498031}
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