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Simplifying 2x2 + 9x = 207 Reorder the terms: 9x + 2x2 = 207 Solving 9x + 2x2 = 207 Solving for variable 'x'. Reorder the terms: -207 + 9x + 2x2 = 207 + -207 Combine like terms: 207 + -207 = 0 -207 + 9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -103.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '103.5' to each side of the equation. -103.5 + 4.5x + 103.5 + x2 = 0 + 103.5 Reorder the terms: -103.5 + 103.5 + 4.5x + x2 = 0 + 103.5 Combine like terms: -103.5 + 103.5 = 0.0 0.0 + 4.5x + x2 = 0 + 103.5 4.5x + x2 = 0 + 103.5 Combine like terms: 0 + 103.5 = 103.5 4.5x + x2 = 103.5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 103.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 103.5 + 5.0625 Combine like terms: 103.5 + 5.0625 = 108.5625 5.0625 + 4.5x + x2 = 108.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 108.5625 Calculate the square root of the right side: 10.419332992 Break this problem into two subproblems by setting (x + 2.25) equal to 10.419332992 and -10.419332992.Subproblem 1
x + 2.25 = 10.419332992 Simplifying x + 2.25 = 10.419332992 Reorder the terms: 2.25 + x = 10.419332992 Solving 2.25 + x = 10.419332992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 10.419332992 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 10.419332992 + -2.25 x = 10.419332992 + -2.25 Combine like terms: 10.419332992 + -2.25 = 8.169332992 x = 8.169332992 Simplifying x = 8.169332992Subproblem 2
x + 2.25 = -10.419332992 Simplifying x + 2.25 = -10.419332992 Reorder the terms: 2.25 + x = -10.419332992 Solving 2.25 + x = -10.419332992 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -10.419332992 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -10.419332992 + -2.25 x = -10.419332992 + -2.25 Combine like terms: -10.419332992 + -2.25 = -12.669332992 x = -12.669332992 Simplifying x = -12.669332992Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.169332992, -12.669332992}
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