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Simplifying 2x2 + -11x + -32 = 0 Reorder the terms: -32 + -11x + 2x2 = 0 Solving -32 + -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'. -16 + -5.5x + x2 = 0 Move the constant term to the right: Add '16' to each side of the equation. -16 + -5.5x + 16 + x2 = 0 + 16 Reorder the terms: -16 + 16 + -5.5x + x2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -5.5x + x2 = 0 + 16 -5.5x + x2 = 0 + 16 Combine like terms: 0 + 16 = 16 -5.5x + x2 = 16 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 = 16 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 16 + 7.5625 Combine like terms: 16 + 7.5625 = 23.5625 7.5625 + -5.5x + x2 = 23.5625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 23.5625 Calculate the square root of the right side: 4.85412196 Break this problem into two subproblems by setting (x + -2.75) equal to 4.85412196 and -4.85412196.Subproblem 1
x + -2.75 = 4.85412196 Simplifying x + -2.75 = 4.85412196 Reorder the terms: -2.75 + x = 4.85412196 Solving -2.75 + x = 4.85412196 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 = 4.85412196 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 4.85412196 + 2.75 x = 4.85412196 + 2.75 Combine like terms: 4.85412196 + 2.75 = 7.60412196 x = 7.60412196 Simplifying x = 7.60412196Subproblem 2
x + -2.75 = -4.85412196 Simplifying x + -2.75 = -4.85412196 Reorder the terms: -2.75 + x = -4.85412196 Solving -2.75 + x = -4.85412196 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 = -4.85412196 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -4.85412196 + 2.75 x = -4.85412196 + 2.75 Combine like terms: -4.85412196 + 2.75 = -2.10412196 x = -2.10412196 Simplifying x = -2.10412196Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.60412196, -2.10412196}
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