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Simplifying x2 + 5.5x + 6 = 0 Reorder the terms: 6 + 5.5x + x2 = 0 Solving 6 + 5.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-6' to each side of the equation. 6 + 5.5x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + 5.5x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 5.5x + x2 = 0 + -6 5.5x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 5.5x + x2 = -6 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 = -6 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = -6 + 7.5625 Combine like terms: -6 + 7.5625 = 1.5625 7.5625 + 5.5x + x2 = 1.5625 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 1.5625 Calculate the square root of the right side: 1.25 Break this problem into two subproblems by setting (x + 2.75) equal to 1.25 and -1.25.Subproblem 1
x + 2.75 = 1.25 Simplifying x + 2.75 = 1.25 Reorder the terms: 2.75 + x = 1.25 Solving 2.75 + x = 1.25 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 = 1.25 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 1.25 + -2.75 x = 1.25 + -2.75 Combine like terms: 1.25 + -2.75 = -1.5 x = -1.5 Simplifying x = -1.5Subproblem 2
x + 2.75 = -1.25 Simplifying x + 2.75 = -1.25 Reorder the terms: 2.75 + x = -1.25 Solving 2.75 + x = -1.25 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 = -1.25 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -1.25 + -2.75 x = -1.25 + -2.75 Combine like terms: -1.25 + -2.75 = -4 x = -4 Simplifying x = -4Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.5, -4}
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