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Simplifying x2 + -3.968x + 0.5088 = 0 Reorder the terms: 0.5088 + -3.968x + x2 = 0 Solving 0.5088 + -3.968x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.5088' to each side of the equation. 0.5088 + -3.968x + -0.5088 + x2 = 0 + -0.5088 Reorder the terms: 0.5088 + -0.5088 + -3.968x + x2 = 0 + -0.5088 Combine like terms: 0.5088 + -0.5088 = 0.0000 0.0000 + -3.968x + x2 = 0 + -0.5088 -3.968x + x2 = 0 + -0.5088 Combine like terms: 0 + -0.5088 = -0.5088 -3.968x + x2 = -0.5088 The x term is -3.968x. Take half its coefficient (-1.984). Square it (3.936256) and add it to both sides. Add '3.936256' to each side of the equation. -3.968x + 3.936256 + x2 = -0.5088 + 3.936256 Reorder the terms: 3.936256 + -3.968x + x2 = -0.5088 + 3.936256 Combine like terms: -0.5088 + 3.936256 = 3.427456 3.936256 + -3.968x + x2 = 3.427456 Factor a perfect square on the left side: (x + -1.984)(x + -1.984) = 3.427456 Calculate the square root of the right side: 1.851338975 Break this problem into two subproblems by setting (x + -1.984) equal to 1.851338975 and -1.851338975.Subproblem 1
x + -1.984 = 1.851338975 Simplifying x + -1.984 = 1.851338975 Reorder the terms: -1.984 + x = 1.851338975 Solving -1.984 + x = 1.851338975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.984' to each side of the equation. -1.984 + 1.984 + x = 1.851338975 + 1.984 Combine like terms: -1.984 + 1.984 = 0.000 0.000 + x = 1.851338975 + 1.984 x = 1.851338975 + 1.984 Combine like terms: 1.851338975 + 1.984 = 3.835338975 x = 3.835338975 Simplifying x = 3.835338975Subproblem 2
x + -1.984 = -1.851338975 Simplifying x + -1.984 = -1.851338975 Reorder the terms: -1.984 + x = -1.851338975 Solving -1.984 + x = -1.851338975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.984' to each side of the equation. -1.984 + 1.984 + x = -1.851338975 + 1.984 Combine like terms: -1.984 + 1.984 = 0.000 0.000 + x = -1.851338975 + 1.984 x = -1.851338975 + 1.984 Combine like terms: -1.851338975 + 1.984 = 0.132661025 x = 0.132661025 Simplifying x = 0.132661025Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.835338975, 0.132661025}
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