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Simplifying x2 = 22x + 42 Reorder the terms: x2 = 42 + 22x Solving x2 = 42 + 22x Solving for variable 'x'. Reorder the terms: -42 + -22x + x2 = 42 + 22x + -42 + -22x Reorder the terms: -42 + -22x + x2 = 42 + -42 + 22x + -22x Combine like terms: 42 + -42 = 0 -42 + -22x + x2 = 0 + 22x + -22x -42 + -22x + x2 = 22x + -22x Combine like terms: 22x + -22x = 0 -42 + -22x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '42' to each side of the equation. -42 + -22x + 42 + x2 = 0 + 42 Reorder the terms: -42 + 42 + -22x + x2 = 0 + 42 Combine like terms: -42 + 42 = 0 0 + -22x + x2 = 0 + 42 -22x + x2 = 0 + 42 Combine like terms: 0 + 42 = 42 -22x + x2 = 42 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 = 42 + 121 Reorder the terms: 121 + -22x + x2 = 42 + 121 Combine like terms: 42 + 121 = 163 121 + -22x + x2 = 163 Factor a perfect square on the left side: (x + -11)(x + -11) = 163 Calculate the square root of the right side: 12.767145335 Break this problem into two subproblems by setting (x + -11) equal to 12.767145335 and -12.767145335.Subproblem 1
x + -11 = 12.767145335 Simplifying x + -11 = 12.767145335 Reorder the terms: -11 + x = 12.767145335 Solving -11 + x = 12.767145335 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 = 12.767145335 + 11 Combine like terms: -11 + 11 = 0 0 + x = 12.767145335 + 11 x = 12.767145335 + 11 Combine like terms: 12.767145335 + 11 = 23.767145335 x = 23.767145335 Simplifying x = 23.767145335Subproblem 2
x + -11 = -12.767145335 Simplifying x + -11 = -12.767145335 Reorder the terms: -11 + x = -12.767145335 Solving -11 + x = -12.767145335 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 = -12.767145335 + 11 Combine like terms: -11 + 11 = 0 0 + x = -12.767145335 + 11 x = -12.767145335 + 11 Combine like terms: -12.767145335 + 11 = -1.767145335 x = -1.767145335 Simplifying x = -1.767145335Solution
The solution to the problem is based on the solutions from the subproblems. x = {23.767145335, -1.767145335}
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