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Simplifying (3 + -1x)(0.25 + -1x) = 0 Multiply (3 + -1x) * (0.25 + -1x) (3(0.25 + -1x) + -1x * (0.25 + -1x)) = 0 ((0.25 * 3 + -1x * 3) + -1x * (0.25 + -1x)) = 0 ((0.75 + -3x) + -1x * (0.25 + -1x)) = 0 (0.75 + -3x + (0.25 * -1x + -1x * -1x)) = 0 (0.75 + -3x + (-0.25x + 1x2)) = 0 Combine like terms: -3x + -0.25x = -3.25x (0.75 + -3.25x + 1x2) = 0 Solving 0.75 + -3.25x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.75' to each side of the equation. 0.75 + -3.25x + -0.75 + x2 = 0 + -0.75 Reorder the terms: 0.75 + -0.75 + -3.25x + x2 = 0 + -0.75 Combine like terms: 0.75 + -0.75 = 0.00 0.00 + -3.25x + x2 = 0 + -0.75 -3.25x + x2 = 0 + -0.75 Combine like terms: 0 + -0.75 = -0.75 -3.25x + x2 = -0.75 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = -0.75 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = -0.75 + 2.640625 Combine like terms: -0.75 + 2.640625 = 1.890625 2.640625 + -3.25x + x2 = 1.890625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 1.890625 Calculate the square root of the right side: 1.375 Break this problem into two subproblems by setting (x + -1.625) equal to 1.375 and -1.375.Subproblem 1
x + -1.625 = 1.375 Simplifying x + -1.625 = 1.375 Reorder the terms: -1.625 + x = 1.375 Solving -1.625 + x = 1.375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 1.375 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 1.375 + 1.625 x = 1.375 + 1.625 Combine like terms: 1.375 + 1.625 = 3 x = 3 Simplifying x = 3Subproblem 2
x + -1.625 = -1.375 Simplifying x + -1.625 = -1.375 Reorder the terms: -1.625 + x = -1.375 Solving -1.625 + x = -1.375 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -1.375 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -1.375 + 1.625 x = -1.375 + 1.625 Combine like terms: -1.375 + 1.625 = 0.25 x = 0.25 Simplifying x = 0.25Solution
The solution to the problem is based on the solutions from the subproblems. x = {3, 0.25}
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