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Simplifying 0 = 2x2 + 11x + -9 Reorder the terms: 0 = -9 + 11x + 2x2 Solving 0 = -9 + 11x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 9 = 9 9 + -11x + -2x2 = -9 + 11x + 2x2 + 9 + -11x + -2x2 Reorder the terms: 9 + -11x + -2x2 = -9 + 9 + 11x + -11x + 2x2 + -2x2 Combine like terms: -9 + 9 = 0 9 + -11x + -2x2 = 0 + 11x + -11x + 2x2 + -2x2 9 + -11x + -2x2 = 11x + -11x + 2x2 + -2x2 Combine like terms: 11x + -11x = 0 9 + -11x + -2x2 = 0 + 2x2 + -2x2 9 + -11x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 9 + -11x + -2x2 = 0 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 = 0.723110997 x = 0.723110997 Simplifying x = 0.723110997Subproblem 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 = -6.223110997 x = -6.223110997 Simplifying x = -6.223110997Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.723110997, -6.223110997}
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