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Simplifying 2x2 + (-11x) + (-9) = 0 2x2 + (-11x) + -9 = 0 Reorder the terms: -9 + (-11x) + 2x2 = 0 Solving -9 + (-11x) + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -4.5 + (-5.5x) + x2 = 0 Move the constant term to the right: Add '4.5' to each side of the equation. -4.5 + (-5.5x) + 4.5 + x2 = 0 + 4.5 Reorder the terms: -4.5 + 4.5 + (-5.5x) + x2 = 0 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + (-5.5x) + x2 = 0 + 4.5 (-5.5x) + x2 = 0 + 4.5 Combine like terms: 0 + 4.5 = 4.5 (-5.5x) + x2 = 4.5 The x term is (-5.5x). Take half its coefficient (-2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. (-5.5x) + 7.5625 + x2 = 4.5 + 7.5625 Reorder the terms: 7.5625 + (-5.5x) + x2 = 4.5 + 7.5625 Combine like terms: 4.5 + 7.5625 = 12.0625 7.5625 + (-5.5x) + x2 = 12.0625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 12.0625 Calculate the square root of the right side: 3.473110997 Break this problem into two subproblems by setting (x + -2.75) equal to 3.473110997 and -3.473110997.Subproblem 1
x + -2.75 = 3.473110997 Simplifying x + -2.75 = 3.473110997 Reorder the terms: -2.75 + x = 3.473110997 Solving -2.75 + x = 3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = 3.473110997 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 3.473110997 + 2.75 x = 3.473110997 + 2.75 Combine like terms: 3.473110997 + 2.75 = 6.223110997 x = 6.223110997 Simplifying x = 6.223110997Subproblem 2
x + -2.75 = -3.473110997 Simplifying x + -2.75 = -3.473110997 Reorder the terms: -2.75 + x = -3.473110997 Solving -2.75 + x = -3.473110997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.75' to each side of the equation. -2.75 + 2.75 + x = -3.473110997 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -3.473110997 + 2.75 x = -3.473110997 + 2.75 Combine like terms: -3.473110997 + 2.75 = -0.723110997 x = -0.723110997 Simplifying x = -0.723110997Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.223110997, -0.723110997}
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