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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 = 4 x = 4 Simplifying x = 4Subproblem 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 = 1.5 x = 1.5 Simplifying x = 1.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {4, 1.5}
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