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Simplifying x2 + -11x = 9 Reorder the terms: -11x + x2 = 9 Solving -11x + x2 = 9 Solving for variable 'x'. Reorder the terms: -9 + -11x + x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -9 + -11x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + -11x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + -11x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -11x + x2 = 0 + 9 -11x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -11x + x2 = 9 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 9 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 9 + 30.25 Combine like terms: 9 + 30.25 = 39.25 30.25 + -11x + x2 = 39.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 39.25 Calculate the square root of the right side: 6.264982043 Break this problem into two subproblems by setting (x + -5.5) equal to 6.264982043 and -6.264982043.Subproblem 1
x + -5.5 = 6.264982043 Simplifying x + -5.5 = 6.264982043 Reorder the terms: -5.5 + x = 6.264982043 Solving -5.5 + x = 6.264982043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 6.264982043 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 6.264982043 + 5.5 x = 6.264982043 + 5.5 Combine like terms: 6.264982043 + 5.5 = 11.764982043 x = 11.764982043 Simplifying x = 11.764982043Subproblem 2
x + -5.5 = -6.264982043 Simplifying x + -5.5 = -6.264982043 Reorder the terms: -5.5 + x = -6.264982043 Solving -5.5 + x = -6.264982043 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -6.264982043 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -6.264982043 + 5.5 x = -6.264982043 + 5.5 Combine like terms: -6.264982043 + 5.5 = -0.764982043 x = -0.764982043 Simplifying x = -0.764982043Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.764982043, -0.764982043}
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