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Simplifying (2x2) + 21x + -6.1 = 0 Reorder the terms: -6.1 + 21x + (2x2) = 0 Solving -6.1 + 21x + (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'. -3.05 + 10.5x + x2 = 0 Move the constant term to the right: Add '3.05' to each side of the equation. -3.05 + 10.5x + 3.05 + x2 = 0 + 3.05 Reorder the terms: -3.05 + 3.05 + 10.5x + x2 = 0 + 3.05 Combine like terms: -3.05 + 3.05 = 0.00 0.00 + 10.5x + x2 = 0 + 3.05 10.5x + x2 = 0 + 3.05 Combine like terms: 0 + 3.05 = 3.05 10.5x + x2 = 3.05 The x term is 10.5x. Take half its coefficient (5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. 10.5x + 27.5625 + x2 = 3.05 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = 3.05 + 27.5625 Combine like terms: 3.05 + 27.5625 = 30.6125 27.5625 + 10.5x + x2 = 30.6125 Factor a perfect square on the left side: ((x) + 5.25)((x) + 5.25) = 30.6125 Calculate the square root of the right side: 5.532856405 Break this problem into two subproblems by setting ((x) + 5.25) equal to 5.532856405 and -5.532856405.Subproblem 1
(x) + 5.25 = 5.532856405 Simplifying (x) + 5.25 = 5.532856405 x + 5.25 = 5.532856405 Reorder the terms: 5.25 + x = 5.532856405 Solving 5.25 + x = 5.532856405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = 5.532856405 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 5.532856405 + -5.25 x = 5.532856405 + -5.25 Combine like terms: 5.532856405 + -5.25 = 0.282856405 x = 0.282856405 Simplifying x = 0.282856405Subproblem 2
(x) + 5.25 = -5.532856405 Simplifying (x) + 5.25 = -5.532856405 x + 5.25 = -5.532856405 Reorder the terms: 5.25 + x = -5.532856405 Solving 5.25 + x = -5.532856405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.25' to each side of the equation. 5.25 + -5.25 + x = -5.532856405 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -5.532856405 + -5.25 x = -5.532856405 + -5.25 Combine like terms: -5.532856405 + -5.25 = -10.782856405 x = -10.782856405 Simplifying x = -10.782856405Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.282856405, -10.782856405}
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