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Simplifying x2 + -5.5x + -3 = 0 Reorder the terms: -3 + -5.5x + x2 = 0 Solving -3 + -5.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -5.5x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -5.5x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5.5x + x2 = 0 + 3 -5.5x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -5.5x + x2 = 3 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 = 3 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 3 + 7.5625 Combine like terms: 3 + 7.5625 = 10.5625 7.5625 + -5.5x + x2 = 10.5625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 10.5625 Calculate the square root of the right side: 3.25 Break this problem into two subproblems by setting (x + -2.75) equal to 3.25 and -3.25.Subproblem 1
x + -2.75 = 3.25 Simplifying x + -2.75 = 3.25 Reorder the terms: -2.75 + x = 3.25 Solving -2.75 + x = 3.25 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 = 3.25 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 3.25 + 2.75 x = 3.25 + 2.75 Combine like terms: 3.25 + 2.75 = 6 x = 6 Simplifying x = 6Subproblem 2
x + -2.75 = -3.25 Simplifying x + -2.75 = -3.25 Reorder the terms: -2.75 + x = -3.25 Solving -2.75 + x = -3.25 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 = -3.25 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -3.25 + 2.75 x = -3.25 + 2.75 Combine like terms: -3.25 + 2.75 = -0.5 x = -0.5 Simplifying x = -0.5Solution
The solution to the problem is based on the solutions from the subproblems. x = {6, -0.5}
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