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Simplifying x2 + -2.4x + 0.96 = 0 Reorder the terms: 0.96 + -2.4x + x2 = 0 Solving 0.96 + -2.4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-0.96' to each side of the equation. 0.96 + -2.4x + -0.96 + x2 = 0 + -0.96 Reorder the terms: 0.96 + -0.96 + -2.4x + x2 = 0 + -0.96 Combine like terms: 0.96 + -0.96 = 0.00 0.00 + -2.4x + x2 = 0 + -0.96 -2.4x + x2 = 0 + -0.96 Combine like terms: 0 + -0.96 = -0.96 -2.4x + x2 = -0.96 The x term is -2.4x. Take half its coefficient (-1.2). Square it (1.44) and add it to both sides. Add '1.44' to each side of the equation. -2.4x + 1.44 + x2 = -0.96 + 1.44 Reorder the terms: 1.44 + -2.4x + x2 = -0.96 + 1.44 Combine like terms: -0.96 + 1.44 = 0.48 1.44 + -2.4x + x2 = 0.48 Factor a perfect square on the left side: (x + -1.2)(x + -1.2) = 0.48 Calculate the square root of the right side: 0.692820323 Break this problem into two subproblems by setting (x + -1.2) equal to 0.692820323 and -0.692820323.Subproblem 1
x + -1.2 = 0.692820323 Simplifying x + -1.2 = 0.692820323 Reorder the terms: -1.2 + x = 0.692820323 Solving -1.2 + x = 0.692820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = 0.692820323 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = 0.692820323 + 1.2 x = 0.692820323 + 1.2 Combine like terms: 0.692820323 + 1.2 = 1.892820323 x = 1.892820323 Simplifying x = 1.892820323Subproblem 2
x + -1.2 = -0.692820323 Simplifying x + -1.2 = -0.692820323 Reorder the terms: -1.2 + x = -0.692820323 Solving -1.2 + x = -0.692820323 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.2' to each side of the equation. -1.2 + 1.2 + x = -0.692820323 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + x = -0.692820323 + 1.2 x = -0.692820323 + 1.2 Combine like terms: -0.692820323 + 1.2 = 0.507179677 x = 0.507179677 Simplifying x = 0.507179677Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.892820323, 0.507179677}
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