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Simplifying 4.38x2 + -3.43x + -5.41 = 0 Reorder the terms: -5.41 + -3.43x + 4.38x2 = 0 Solving -5.41 + -3.43x + 4.38x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.38 the coefficient of the squared term: Divide each side by '4.38'. -1.235159817 + -0.7831050228x + x2 = 0 Move the constant term to the right: Add '1.235159817' to each side of the equation. -1.235159817 + -0.7831050228x + 1.235159817 + x2 = 0 + 1.235159817 Reorder the terms: -1.235159817 + 1.235159817 + -0.7831050228x + x2 = 0 + 1.235159817 Combine like terms: -1.235159817 + 1.235159817 = 0.000000000 0.000000000 + -0.7831050228x + x2 = 0 + 1.235159817 -0.7831050228x + x2 = 0 + 1.235159817 Combine like terms: 0 + 1.235159817 = 1.235159817 -0.7831050228x + x2 = 1.235159817 The x term is -0.7831050228x. Take half its coefficient (-0.3915525114). Square it (0.1533133692) and add it to both sides. Add '0.1533133692' to each side of the equation. -0.7831050228x + 0.1533133692 + x2 = 1.235159817 + 0.1533133692 Reorder the terms: 0.1533133692 + -0.7831050228x + x2 = 1.235159817 + 0.1533133692 Combine like terms: 1.235159817 + 0.1533133692 = 1.3884731862 0.1533133692 + -0.7831050228x + x2 = 1.3884731862 Factor a perfect square on the left side: (x + -0.3915525114)(x + -0.3915525114) = 1.3884731862 Calculate the square root of the right side: 1.178334921 Break this problem into two subproblems by setting (x + -0.3915525114) equal to 1.178334921 and -1.178334921.Subproblem 1
x + -0.3915525114 = 1.178334921 Simplifying x + -0.3915525114 = 1.178334921 Reorder the terms: -0.3915525114 + x = 1.178334921 Solving -0.3915525114 + x = 1.178334921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3915525114' to each side of the equation. -0.3915525114 + 0.3915525114 + x = 1.178334921 + 0.3915525114 Combine like terms: -0.3915525114 + 0.3915525114 = 0.0000000000 0.0000000000 + x = 1.178334921 + 0.3915525114 x = 1.178334921 + 0.3915525114 Combine like terms: 1.178334921 + 0.3915525114 = 1.5698874324 x = 1.5698874324 Simplifying x = 1.5698874324Subproblem 2
x + -0.3915525114 = -1.178334921 Simplifying x + -0.3915525114 = -1.178334921 Reorder the terms: -0.3915525114 + x = -1.178334921 Solving -0.3915525114 + x = -1.178334921 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3915525114' to each side of the equation. -0.3915525114 + 0.3915525114 + x = -1.178334921 + 0.3915525114 Combine like terms: -0.3915525114 + 0.3915525114 = 0.0000000000 0.0000000000 + x = -1.178334921 + 0.3915525114 x = -1.178334921 + 0.3915525114 Combine like terms: -1.178334921 + 0.3915525114 = -0.7867824096 x = -0.7867824096 Simplifying x = -0.7867824096Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.5698874324, -0.7867824096}
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