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Simplifying x2 + -22x + -30 = 0 Reorder the terms: -30 + -22x + x2 = 0 Solving -30 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + -22x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + -22x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + -22x + x2 = 0 + 30 -22x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 -22x + x2 = 30 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 = 30 + 121 Reorder the terms: 121 + -22x + x2 = 30 + 121 Combine like terms: 30 + 121 = 151 121 + -22x + x2 = 151 Factor a perfect square on the left side: (x + -11)(x + -11) = 151 Calculate the square root of the right side: 12.288205727 Break this problem into two subproblems by setting (x + -11) equal to 12.288205727 and -12.288205727.Subproblem 1
x + -11 = 12.288205727 Simplifying x + -11 = 12.288205727 Reorder the terms: -11 + x = 12.288205727 Solving -11 + x = 12.288205727 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 = 12.288205727 + 11 Combine like terms: -11 + 11 = 0 0 + x = 12.288205727 + 11 x = 12.288205727 + 11 Combine like terms: 12.288205727 + 11 = 23.288205727 x = 23.288205727 Simplifying x = 23.288205727Subproblem 2
x + -11 = -12.288205727 Simplifying x + -11 = -12.288205727 Reorder the terms: -11 + x = -12.288205727 Solving -11 + x = -12.288205727 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 = -12.288205727 + 11 Combine like terms: -11 + 11 = 0 0 + x = -12.288205727 + 11 x = -12.288205727 + 11 Combine like terms: -12.288205727 + 11 = -1.288205727 x = -1.288205727 Simplifying x = -1.288205727Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.288205727, -1.288205727}
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