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Simplifying 10x2 + -41x = 21 Reorder the terms: -41x + 10x2 = 21 Solving -41x + 10x2 = 21 Solving for variable 'x'. Reorder the terms: -21 + -41x + 10x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + -41x + 10x2 = 0 Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -2.1 + -4.1x + x2 = 0 Move the constant term to the right: Add '2.1' to each side of the equation. -2.1 + -4.1x + 2.1 + x2 = 0 + 2.1 Reorder the terms: -2.1 + 2.1 + -4.1x + x2 = 0 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + -4.1x + x2 = 0 + 2.1 -4.1x + x2 = 0 + 2.1 Combine like terms: 0 + 2.1 = 2.1 -4.1x + x2 = 2.1 The x term is -4.1x. Take half its coefficient (-2.05). Square it (4.2025) and add it to both sides. Add '4.2025' to each side of the equation. -4.1x + 4.2025 + x2 = 2.1 + 4.2025 Reorder the terms: 4.2025 + -4.1x + x2 = 2.1 + 4.2025 Combine like terms: 2.1 + 4.2025 = 6.3025 4.2025 + -4.1x + x2 = 6.3025 Factor a perfect square on the left side: (x + -2.05)(x + -2.05) = 6.3025 Calculate the square root of the right side: 2.510478042 Break this problem into two subproblems by setting (x + -2.05) equal to 2.510478042 and -2.510478042.Subproblem 1
x + -2.05 = 2.510478042 Simplifying x + -2.05 = 2.510478042 Reorder the terms: -2.05 + x = 2.510478042 Solving -2.05 + x = 2.510478042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.05' to each side of the equation. -2.05 + 2.05 + x = 2.510478042 + 2.05 Combine like terms: -2.05 + 2.05 = 0.00 0.00 + x = 2.510478042 + 2.05 x = 2.510478042 + 2.05 Combine like terms: 2.510478042 + 2.05 = 4.560478042 x = 4.560478042 Simplifying x = 4.560478042Subproblem 2
x + -2.05 = -2.510478042 Simplifying x + -2.05 = -2.510478042 Reorder the terms: -2.05 + x = -2.510478042 Solving -2.05 + x = -2.510478042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.05' to each side of the equation. -2.05 + 2.05 + x = -2.510478042 + 2.05 Combine like terms: -2.05 + 2.05 = 0.00 0.00 + x = -2.510478042 + 2.05 x = -2.510478042 + 2.05 Combine like terms: -2.510478042 + 2.05 = -0.460478042 x = -0.460478042 Simplifying x = -0.460478042Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.560478042, -0.460478042}
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