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Simplifying 2x2 + 21x + 5.5 = 0 Reorder the terms: 5.5 + 21x + 2x2 = 0 Solving 5.5 + 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'. 2.75 + 10.5x + x2 = 0 Move the constant term to the right: Add '-2.75' to each side of the equation. 2.75 + 10.5x + -2.75 + x2 = 0 + -2.75 Reorder the terms: 2.75 + -2.75 + 10.5x + x2 = 0 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + 10.5x + x2 = 0 + -2.75 10.5x + x2 = 0 + -2.75 Combine like terms: 0 + -2.75 = -2.75 10.5x + x2 = -2.75 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 = -2.75 + 27.5625 Reorder the terms: 27.5625 + 10.5x + x2 = -2.75 + 27.5625 Combine like terms: -2.75 + 27.5625 = 24.8125 27.5625 + 10.5x + x2 = 24.8125 Factor a perfect square on the left side: (x + 5.25)(x + 5.25) = 24.8125 Calculate the square root of the right side: 4.981214711 Break this problem into two subproblems by setting (x + 5.25) equal to 4.981214711 and -4.981214711.Subproblem 1
x + 5.25 = 4.981214711 Simplifying x + 5.25 = 4.981214711 Reorder the terms: 5.25 + x = 4.981214711 Solving 5.25 + x = 4.981214711 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 = 4.981214711 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = 4.981214711 + -5.25 x = 4.981214711 + -5.25 Combine like terms: 4.981214711 + -5.25 = -0.268785289 x = -0.268785289 Simplifying x = -0.268785289Subproblem 2
x + 5.25 = -4.981214711 Simplifying x + 5.25 = -4.981214711 Reorder the terms: 5.25 + x = -4.981214711 Solving 5.25 + x = -4.981214711 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 = -4.981214711 + -5.25 Combine like terms: 5.25 + -5.25 = 0.00 0.00 + x = -4.981214711 + -5.25 x = -4.981214711 + -5.25 Combine like terms: -4.981214711 + -5.25 = -10.231214711 x = -10.231214711 Simplifying x = -10.231214711Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.268785289, -10.231214711}
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