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Simplifying x2 + -22x + -54 = 0 Reorder the terms: -54 + -22x + x2 = 0 Solving -54 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '54' to each side of the equation. -54 + -22x + 54 + x2 = 0 + 54 Reorder the terms: -54 + 54 + -22x + x2 = 0 + 54 Combine like terms: -54 + 54 = 0 0 + -22x + x2 = 0 + 54 -22x + x2 = 0 + 54 Combine like terms: 0 + 54 = 54 -22x + x2 = 54 The x term is -22x. Take half its coefficient (-11). Square it (121) and add it to both sides. Add '121' to each side of the equation. -22x + 121 + x2 = 54 + 121 Reorder the terms: 121 + -22x + x2 = 54 + 121 Combine like terms: 54 + 121 = 175 121 + -22x + x2 = 175 Factor a perfect square on the left side: (x + -11)(x + -11) = 175 Calculate the square root of the right side: 13.228756555 Break this problem into two subproblems by setting (x + -11) equal to 13.228756555 and -13.228756555.Subproblem 1
x + -11 = 13.228756555 Simplifying x + -11 = 13.228756555 Reorder the terms: -11 + x = 13.228756555 Solving -11 + x = 13.228756555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = 13.228756555 + 11 Combine like terms: -11 + 11 = 0 0 + x = 13.228756555 + 11 x = 13.228756555 + 11 Combine like terms: 13.228756555 + 11 = 24.228756555 x = 24.228756555 Simplifying x = 24.228756555Subproblem 2
x + -11 = -13.228756555 Simplifying x + -11 = -13.228756555 Reorder the terms: -11 + x = -13.228756555 Solving -11 + x = -13.228756555 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + x = -13.228756555 + 11 Combine like terms: -11 + 11 = 0 0 + x = -13.228756555 + 11 x = -13.228756555 + 11 Combine like terms: -13.228756555 + 11 = -2.228756555 x = -2.228756555 Simplifying x = -2.228756555Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.228756555, -2.228756555}
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