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Simplifying 2x2 + -6x + 0.25 = 0 Reorder the terms: 0.25 + -6x + 2x2 = 0 Solving 0.25 + -6x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 0.125 + -3x + x2 = 0 Move the constant term to the right: Add '-0.125' to each side of the equation. 0.125 + -3x + -0.125 + x2 = 0 + -0.125 Reorder the terms: 0.125 + -0.125 + -3x + x2 = 0 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + -3x + x2 = 0 + -0.125 -3x + x2 = 0 + -0.125 Combine like terms: 0 + -0.125 = -0.125 -3x + x2 = -0.125 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = -0.125 + 2.25 Reorder the terms: 2.25 + -3x + x2 = -0.125 + 2.25 Combine like terms: -0.125 + 2.25 = 2.125 2.25 + -3x + x2 = 2.125 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 2.125 Calculate the square root of the right side: 1.457737974 Break this problem into two subproblems by setting (x + -1.5) equal to 1.457737974 and -1.457737974.Subproblem 1
x + -1.5 = 1.457737974 Simplifying x + -1.5 = 1.457737974 Reorder the terms: -1.5 + x = 1.457737974 Solving -1.5 + x = 1.457737974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.457737974 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.457737974 + 1.5 x = 1.457737974 + 1.5 Combine like terms: 1.457737974 + 1.5 = 2.957737974 x = 2.957737974 Simplifying x = 2.957737974Subproblem 2
x + -1.5 = -1.457737974 Simplifying x + -1.5 = -1.457737974 Reorder the terms: -1.5 + x = -1.457737974 Solving -1.5 + x = -1.457737974 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.457737974 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.457737974 + 1.5 x = -1.457737974 + 1.5 Combine like terms: -1.457737974 + 1.5 = 0.042262026 x = 0.042262026 Simplifying x = 0.042262026Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.957737974, 0.042262026}
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