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Simplifying 20x + 9x2 = 28 Solving 20x + 9x2 = 28 Solving for variable 'x'. Reorder the terms: -28 + 20x + 9x2 = 28 + -28 Combine like terms: 28 + -28 = 0 -28 + 20x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -3.111111111 + 2.222222222x + x2 = 0 Move the constant term to the right: Add '3.111111111' to each side of the equation. -3.111111111 + 2.222222222x + 3.111111111 + x2 = 0 + 3.111111111 Reorder the terms: -3.111111111 + 3.111111111 + 2.222222222x + x2 = 0 + 3.111111111 Combine like terms: -3.111111111 + 3.111111111 = 0.000000000 0.000000000 + 2.222222222x + x2 = 0 + 3.111111111 2.222222222x + x2 = 0 + 3.111111111 Combine like terms: 0 + 3.111111111 = 3.111111111 2.222222222x + x2 = 3.111111111 The x term is 2.222222222x. Take half its coefficient (1.111111111). Square it (1.234567901) and add it to both sides. Add '1.234567901' to each side of the equation. 2.222222222x + 1.234567901 + x2 = 3.111111111 + 1.234567901 Reorder the terms: 1.234567901 + 2.222222222x + x2 = 3.111111111 + 1.234567901 Combine like terms: 3.111111111 + 1.234567901 = 4.345679012 1.234567901 + 2.222222222x + x2 = 4.345679012 Factor a perfect square on the left side: (x + 1.111111111)(x + 1.111111111) = 4.345679012 Calculate the square root of the right side: 2.084629227 Break this problem into two subproblems by setting (x + 1.111111111) equal to 2.084629227 and -2.084629227.Subproblem 1
x + 1.111111111 = 2.084629227 Simplifying x + 1.111111111 = 2.084629227 Reorder the terms: 1.111111111 + x = 2.084629227 Solving 1.111111111 + x = 2.084629227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.111111111' to each side of the equation. 1.111111111 + -1.111111111 + x = 2.084629227 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + x = 2.084629227 + -1.111111111 x = 2.084629227 + -1.111111111 Combine like terms: 2.084629227 + -1.111111111 = 0.973518116 x = 0.973518116 Simplifying x = 0.973518116Subproblem 2
x + 1.111111111 = -2.084629227 Simplifying x + 1.111111111 = -2.084629227 Reorder the terms: 1.111111111 + x = -2.084629227 Solving 1.111111111 + x = -2.084629227 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.111111111' to each side of the equation. 1.111111111 + -1.111111111 + x = -2.084629227 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + x = -2.084629227 + -1.111111111 x = -2.084629227 + -1.111111111 Combine like terms: -2.084629227 + -1.111111111 = -3.195740338 x = -3.195740338 Simplifying x = -3.195740338Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.973518116, -3.195740338}
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