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Simplifying 2x2 + 11x + -36 = 0 Reorder the terms: -36 + 11x + 2x2 = 0 Solving -36 + 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'. -18 + 5.5x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + 5.5x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + 5.5x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + 5.5x + x2 = 0 + 18 5.5x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 5.5x + x2 = 18 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 = 18 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 18 + 7.5625 Combine like terms: 18 + 7.5625 = 25.5625 7.5625 + 5.5x + x2 = 25.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 25.5625 Calculate the square root of the right side: 5.055937104 Break this problem into two subproblems by setting (x + 2.75) equal to 5.055937104 and -5.055937104.Subproblem 1
x + 2.75 = 5.055937104 Simplifying x + 2.75 = 5.055937104 Reorder the terms: 2.75 + x = 5.055937104 Solving 2.75 + x = 5.055937104 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 = 5.055937104 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 5.055937104 + -2.75 x = 5.055937104 + -2.75 Combine like terms: 5.055937104 + -2.75 = 2.305937104 x = 2.305937104 Simplifying x = 2.305937104Subproblem 2
x + 2.75 = -5.055937104 Simplifying x + 2.75 = -5.055937104 Reorder the terms: 2.75 + x = -5.055937104 Solving 2.75 + x = -5.055937104 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 = -5.055937104 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -5.055937104 + -2.75 x = -5.055937104 + -2.75 Combine like terms: -5.055937104 + -2.75 = -7.805937104 x = -7.805937104 Simplifying x = -7.805937104Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.305937104, -7.805937104}
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