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Simplifying 2x2 + -4x + -10.4 = 0 Reorder the terms: -10.4 + -4x + 2x2 = 0 Solving -10.4 + -4x + 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'. -5.2 + -2x + x2 = 0 Move the constant term to the right: Add '5.2' to each side of the equation. -5.2 + -2x + 5.2 + x2 = 0 + 5.2 Reorder the terms: -5.2 + 5.2 + -2x + x2 = 0 + 5.2 Combine like terms: -5.2 + 5.2 = 0.0 0.0 + -2x + x2 = 0 + 5.2 -2x + x2 = 0 + 5.2 Combine like terms: 0 + 5.2 = 5.2 -2x + x2 = 5.2 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 5.2 + 1 Reorder the terms: 1 + -2x + x2 = 5.2 + 1 Combine like terms: 5.2 + 1 = 6.2 1 + -2x + x2 = 6.2 Factor a perfect square on the left side: (x + -1)(x + -1) = 6.2 Calculate the square root of the right side: 2.48997992 Break this problem into two subproblems by setting (x + -1) equal to 2.48997992 and -2.48997992.Subproblem 1
x + -1 = 2.48997992 Simplifying x + -1 = 2.48997992 Reorder the terms: -1 + x = 2.48997992 Solving -1 + x = 2.48997992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.48997992 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.48997992 + 1 x = 2.48997992 + 1 Combine like terms: 2.48997992 + 1 = 3.48997992 x = 3.48997992 Simplifying x = 3.48997992Subproblem 2
x + -1 = -2.48997992 Simplifying x + -1 = -2.48997992 Reorder the terms: -1 + x = -2.48997992 Solving -1 + x = -2.48997992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.48997992 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.48997992 + 1 x = -2.48997992 + 1 Combine like terms: -2.48997992 + 1 = -1.48997992 x = -1.48997992 Simplifying x = -1.48997992Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.48997992, -1.48997992}
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