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Simplifying x2 + -5.5x + -29 = 0 Reorder the terms: -29 + -5.5x + x2 = 0 Solving -29 + -5.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '29' to each side of the equation. -29 + -5.5x + 29 + x2 = 0 + 29 Reorder the terms: -29 + 29 + -5.5x + x2 = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -5.5x + x2 = 0 + 29 -5.5x + x2 = 0 + 29 Combine like terms: 0 + 29 = 29 -5.5x + x2 = 29 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 = 29 + 7.5625 Reorder the terms: 7.5625 + -5.5x + x2 = 29 + 7.5625 Combine like terms: 29 + 7.5625 = 36.5625 7.5625 + -5.5x + x2 = 36.5625 Factor a perfect square on the left side: (x + -2.75)(x + -2.75) = 36.5625 Calculate the square root of the right side: 6.046693311 Break this problem into two subproblems by setting (x + -2.75) equal to 6.046693311 and -6.046693311.Subproblem 1
x + -2.75 = 6.046693311 Simplifying x + -2.75 = 6.046693311 Reorder the terms: -2.75 + x = 6.046693311 Solving -2.75 + x = 6.046693311 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 = 6.046693311 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = 6.046693311 + 2.75 x = 6.046693311 + 2.75 Combine like terms: 6.046693311 + 2.75 = 8.796693311 x = 8.796693311 Simplifying x = 8.796693311Subproblem 2
x + -2.75 = -6.046693311 Simplifying x + -2.75 = -6.046693311 Reorder the terms: -2.75 + x = -6.046693311 Solving -2.75 + x = -6.046693311 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 = -6.046693311 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + x = -6.046693311 + 2.75 x = -6.046693311 + 2.75 Combine like terms: -6.046693311 + 2.75 = -3.296693311 x = -3.296693311 Simplifying x = -3.296693311Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.796693311, -3.296693311}
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