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Simplifying x2 + -22x + -7 = 0 Reorder the terms: -7 + -22x + x2 = 0 Solving -7 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + -22x + 7 + x2 = 0 + 7 Reorder the terms: -7 + 7 + -22x + x2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -22x + x2 = 0 + 7 -22x + x2 = 0 + 7 Combine like terms: 0 + 7 = 7 -22x + x2 = 7 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 = 7 + 121 Reorder the terms: 121 + -22x + x2 = 7 + 121 Combine like terms: 7 + 121 = 128 121 + -22x + x2 = 128 Factor a perfect square on the left side: (x + -11)(x + -11) = 128 Calculate the square root of the right side: 11.313708499 Break this problem into two subproblems by setting (x + -11) equal to 11.313708499 and -11.313708499.Subproblem 1
x + -11 = 11.313708499 Simplifying x + -11 = 11.313708499 Reorder the terms: -11 + x = 11.313708499 Solving -11 + x = 11.313708499 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 = 11.313708499 + 11 Combine like terms: -11 + 11 = 0 0 + x = 11.313708499 + 11 x = 11.313708499 + 11 Combine like terms: 11.313708499 + 11 = 22.313708499 x = 22.313708499 Simplifying x = 22.313708499Subproblem 2
x + -11 = -11.313708499 Simplifying x + -11 = -11.313708499 Reorder the terms: -11 + x = -11.313708499 Solving -11 + x = -11.313708499 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 = -11.313708499 + 11 Combine like terms: -11 + 11 = 0 0 + x = -11.313708499 + 11 x = -11.313708499 + 11 Combine like terms: -11.313708499 + 11 = -0.313708499 x = -0.313708499 Simplifying x = -0.313708499Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.313708499, -0.313708499}
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