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Simplifying 2x2 + -9x + -34 = -11 Reorder the terms: -34 + -9x + 2x2 = -11 Solving -34 + -9x + 2x2 = -11 Solving for variable 'x'. Reorder the terms: -34 + 11 + -9x + 2x2 = -11 + 11 Combine like terms: -34 + 11 = -23 -23 + -9x + 2x2 = -11 + 11 Combine like terms: -11 + 11 = 0 -23 + -9x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -11.5 + -4.5x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -4.5x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -4.5x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -4.5x + x2 = 0 + 11.5 -4.5x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -4.5x + x2 = 11.5 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 = 11.5 + 5.0625 Reorder the terms: 5.0625 + -4.5x + x2 = 11.5 + 5.0625 Combine like terms: 11.5 + 5.0625 = 16.5625 5.0625 + -4.5x + x2 = 16.5625 Factor a perfect square on the left side: (x + -2.25)(x + -2.25) = 16.5625 Calculate the square root of the right side: 4.069705149 Break this problem into two subproblems by setting (x + -2.25) equal to 4.069705149 and -4.069705149.Subproblem 1
x + -2.25 = 4.069705149 Simplifying x + -2.25 = 4.069705149 Reorder the terms: -2.25 + x = 4.069705149 Solving -2.25 + x = 4.069705149 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 = 4.069705149 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = 4.069705149 + 2.25 x = 4.069705149 + 2.25 Combine like terms: 4.069705149 + 2.25 = 6.319705149 x = 6.319705149 Simplifying x = 6.319705149Subproblem 2
x + -2.25 = -4.069705149 Simplifying x + -2.25 = -4.069705149 Reorder the terms: -2.25 + x = -4.069705149 Solving -2.25 + x = -4.069705149 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 = -4.069705149 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + x = -4.069705149 + 2.25 x = -4.069705149 + 2.25 Combine like terms: -4.069705149 + 2.25 = -1.819705149 x = -1.819705149 Simplifying x = -1.819705149Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.319705149, -1.819705149}
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