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Simplifying 9x2 + -28x + -4 = 0 Reorder the terms: -4 + -28x + 9x2 = 0 Solving -4 + -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'. -0.4444444444 + -3.111111111x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + -3.111111111x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + -3.111111111x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + -3.111111111x + x2 = 0 + 0.4444444444 -3.111111111x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 -3.111111111x + x2 = 0.4444444444 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 = 0.4444444444 + 2.419753088 Reorder the terms: 2.419753088 + -3.111111111x + x2 = 0.4444444444 + 2.419753088 Combine like terms: 0.4444444444 + 2.419753088 = 2.8641975324 2.419753088 + -3.111111111x + x2 = 2.8641975324 Factor a perfect square on the left side: (x + -1.555555556)(x + -1.555555556) = 2.8641975324 Calculate the square root of the right side: 1.692394024 Break this problem into two subproblems by setting (x + -1.555555556) equal to 1.692394024 and -1.692394024.Subproblem 1
x + -1.555555556 = 1.692394024 Simplifying x + -1.555555556 = 1.692394024 Reorder the terms: -1.555555556 + x = 1.692394024 Solving -1.555555556 + x = 1.692394024 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 = 1.692394024 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + x = 1.692394024 + 1.555555556 x = 1.692394024 + 1.555555556 Combine like terms: 1.692394024 + 1.555555556 = 3.24794958 x = 3.24794958 Simplifying x = 3.24794958Subproblem 2
x + -1.555555556 = -1.692394024 Simplifying x + -1.555555556 = -1.692394024 Reorder the terms: -1.555555556 + x = -1.692394024 Solving -1.555555556 + x = -1.692394024 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 = -1.692394024 + 1.555555556 Combine like terms: -1.555555556 + 1.555555556 = 0.000000000 0.000000000 + x = -1.692394024 + 1.555555556 x = -1.692394024 + 1.555555556 Combine like terms: -1.692394024 + 1.555555556 = -0.136838468 x = -0.136838468 Simplifying x = -0.136838468Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.24794958, -0.136838468}
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