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Simplifying x2 + -11x + -51 = 0 Reorder the terms: -51 + -11x + x2 = 0 Solving -51 + -11x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '51' to each side of the equation. -51 + -11x + 51 + x2 = 0 + 51 Reorder the terms: -51 + 51 + -11x + x2 = 0 + 51 Combine like terms: -51 + 51 = 0 0 + -11x + x2 = 0 + 51 -11x + x2 = 0 + 51 Combine like terms: 0 + 51 = 51 -11x + x2 = 51 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 = 51 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 51 + 30.25 Combine like terms: 51 + 30.25 = 81.25 30.25 + -11x + x2 = 81.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 81.25 Calculate the square root of the right side: 9.013878189 Break this problem into two subproblems by setting (x + -5.5) equal to 9.013878189 and -9.013878189.Subproblem 1
x + -5.5 = 9.013878189 Simplifying x + -5.5 = 9.013878189 Reorder the terms: -5.5 + x = 9.013878189 Solving -5.5 + x = 9.013878189 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 = 9.013878189 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 9.013878189 + 5.5 x = 9.013878189 + 5.5 Combine like terms: 9.013878189 + 5.5 = 14.513878189 x = 14.513878189 Simplifying x = 14.513878189Subproblem 2
x + -5.5 = -9.013878189 Simplifying x + -5.5 = -9.013878189 Reorder the terms: -5.5 + x = -9.013878189 Solving -5.5 + x = -9.013878189 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 = -9.013878189 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -9.013878189 + 5.5 x = -9.013878189 + 5.5 Combine like terms: -9.013878189 + 5.5 = -3.513878189 x = -3.513878189 Simplifying x = -3.513878189Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.513878189, -3.513878189}
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