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Simplifying 9x2 + 28x + -20 = 0 Reorder the terms: -20 + 28x + 9x2 = 0 Solving -20 + 28x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -2.222222222 + 3.111111111x + x2 = 0 Move the constant term to the right: Add '2.222222222' to each side of the equation. -2.222222222 + 3.111111111x + 2.222222222 + x2 = 0 + 2.222222222 Reorder the terms: -2.222222222 + 2.222222222 + 3.111111111x + x2 = 0 + 2.222222222 Combine like terms: -2.222222222 + 2.222222222 = 0.000000000 0.000000000 + 3.111111111x + x2 = 0 + 2.222222222 3.111111111x + x2 = 0 + 2.222222222 Combine like terms: 0 + 2.222222222 = 2.222222222 3.111111111x + x2 = 2.222222222 The x term is 3.111111111x. Take half its coefficient (1.555555556). Square it (2.419753088) and add it to both sides. Add '2.419753088' to each side of the equation. 3.111111111x + 2.419753088 + x2 = 2.222222222 + 2.419753088 Reorder the terms: 2.419753088 + 3.111111111x + x2 = 2.222222222 + 2.419753088 Combine like terms: 2.222222222 + 2.419753088 = 4.64197531 2.419753088 + 3.111111111x + x2 = 4.64197531 Factor a perfect square on the left side: (x + 1.555555556)(x + 1.555555556) = 4.64197531 Calculate the square root of the right side: 2.154524381 Break this problem into two subproblems by setting (x + 1.555555556) equal to 2.154524381 and -2.154524381.Subproblem 1
x + 1.555555556 = 2.154524381 Simplifying x + 1.555555556 = 2.154524381 Reorder the terms: 1.555555556 + x = 2.154524381 Solving 1.555555556 + x = 2.154524381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.555555556' to each side of the equation. 1.555555556 + -1.555555556 + x = 2.154524381 + -1.555555556 Combine like terms: 1.555555556 + -1.555555556 = 0.000000000 0.000000000 + x = 2.154524381 + -1.555555556 x = 2.154524381 + -1.555555556 Combine like terms: 2.154524381 + -1.555555556 = 0.598968825 x = 0.598968825 Simplifying x = 0.598968825Subproblem 2
x + 1.555555556 = -2.154524381 Simplifying x + 1.555555556 = -2.154524381 Reorder the terms: 1.555555556 + x = -2.154524381 Solving 1.555555556 + x = -2.154524381 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.555555556' to each side of the equation. 1.555555556 + -1.555555556 + x = -2.154524381 + -1.555555556 Combine like terms: 1.555555556 + -1.555555556 = 0.000000000 0.000000000 + x = -2.154524381 + -1.555555556 x = -2.154524381 + -1.555555556 Combine like terms: -2.154524381 + -1.555555556 = -3.710079937 x = -3.710079937 Simplifying x = -3.710079937Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.598968825, -3.710079937}
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