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Simplifying x2 + -22x + 66 = 0 Reorder the terms: 66 + -22x + x2 = 0 Solving 66 + -22x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-66' to each side of the equation. 66 + -22x + -66 + x2 = 0 + -66 Reorder the terms: 66 + -66 + -22x + x2 = 0 + -66 Combine like terms: 66 + -66 = 0 0 + -22x + x2 = 0 + -66 -22x + x2 = 0 + -66 Combine like terms: 0 + -66 = -66 -22x + x2 = -66 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 = -66 + 121 Reorder the terms: 121 + -22x + x2 = -66 + 121 Combine like terms: -66 + 121 = 55 121 + -22x + x2 = 55 Factor a perfect square on the left side: (x + -11)(x + -11) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (x + -11) equal to 7.416198487 and -7.416198487.Subproblem 1
x + -11 = 7.416198487 Simplifying x + -11 = 7.416198487 Reorder the terms: -11 + x = 7.416198487 Solving -11 + x = 7.416198487 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 = 7.416198487 + 11 Combine like terms: -11 + 11 = 0 0 + x = 7.416198487 + 11 x = 7.416198487 + 11 Combine like terms: 7.416198487 + 11 = 18.416198487 x = 18.416198487 Simplifying x = 18.416198487Subproblem 2
x + -11 = -7.416198487 Simplifying x + -11 = -7.416198487 Reorder the terms: -11 + x = -7.416198487 Solving -11 + x = -7.416198487 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 = -7.416198487 + 11 Combine like terms: -11 + 11 = 0 0 + x = -7.416198487 + 11 x = -7.416198487 + 11 Combine like terms: -7.416198487 + 11 = 3.583801513 x = 3.583801513 Simplifying x = 3.583801513Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.416198487, 3.583801513}
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