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Simplifying 0 = 9x2 + 28x + -9 Reorder the terms: 0 = -9 + 28x + 9x2 Solving 0 = -9 + 28x + 9x2 Solving for variable 'x'. Combine like terms: 0 + 9 = 9 9 + -28x + -9x2 = -9 + 28x + 9x2 + 9 + -28x + -9x2 Reorder the terms: 9 + -28x + -9x2 = -9 + 9 + 28x + -28x + 9x2 + -9x2 Combine like terms: -9 + 9 = 0 9 + -28x + -9x2 = 0 + 28x + -28x + 9x2 + -9x2 9 + -28x + -9x2 = 28x + -28x + 9x2 + -9x2 Combine like terms: 28x + -28x = 0 9 + -28x + -9x2 = 0 + 9x2 + -9x2 9 + -28x + -9x2 = 9x2 + -9x2 Combine like terms: 9x2 + -9x2 = 0 9 + -28x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -1 + 3.111111111x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 3.111111111x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 3.111111111x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 3.111111111x + x2 = 0 + 1 3.111111111x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 3.111111111x + x2 = 1 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 = 1 + 2.419753088 Reorder the terms: 2.419753088 + 3.111111111x + x2 = 1 + 2.419753088 Combine like terms: 1 + 2.419753088 = 3.419753088 2.419753088 + 3.111111111x + x2 = 3.419753088 Factor a perfect square on the left side: (x + 1.555555556)(x + 1.555555556) = 3.419753088 Calculate the square root of the right side: 1.849257442 Break this problem into two subproblems by setting (x + 1.555555556) equal to 1.849257442 and -1.849257442.Subproblem 1
x + 1.555555556 = 1.849257442 Simplifying x + 1.555555556 = 1.849257442 Reorder the terms: 1.555555556 + x = 1.849257442 Solving 1.555555556 + x = 1.849257442 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 = 1.849257442 + -1.555555556 Combine like terms: 1.555555556 + -1.555555556 = 0.000000000 0.000000000 + x = 1.849257442 + -1.555555556 x = 1.849257442 + -1.555555556 Combine like terms: 1.849257442 + -1.555555556 = 0.293701886 x = 0.293701886 Simplifying x = 0.293701886Subproblem 2
x + 1.555555556 = -1.849257442 Simplifying x + 1.555555556 = -1.849257442 Reorder the terms: 1.555555556 + x = -1.849257442 Solving 1.555555556 + x = -1.849257442 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 = -1.849257442 + -1.555555556 Combine like terms: 1.555555556 + -1.555555556 = 0.000000000 0.000000000 + x = -1.849257442 + -1.555555556 x = -1.849257442 + -1.555555556 Combine like terms: -1.849257442 + -1.555555556 = -3.404812998 x = -3.404812998 Simplifying x = -3.404812998Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.293701886, -3.404812998}
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