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Simplifying 22x + -51 = x2 + -6x + 9 Reorder the terms: -51 + 22x = x2 + -6x + 9 Reorder the terms: -51 + 22x = 9 + -6x + x2 Solving -51 + 22x = 9 + -6x + x2 Solving for variable 'x'. Reorder the terms: -51 + -9 + 22x + 6x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2 Combine like terms: -51 + -9 = -60 -60 + 22x + 6x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2 Combine like terms: 22x + 6x = 28x -60 + 28x + -1x2 = 9 + -6x + x2 + -9 + 6x + -1x2 Reorder the terms: -60 + 28x + -1x2 = 9 + -9 + -6x + 6x + x2 + -1x2 Combine like terms: 9 + -9 = 0 -60 + 28x + -1x2 = 0 + -6x + 6x + x2 + -1x2 -60 + 28x + -1x2 = -6x + 6x + x2 + -1x2 Combine like terms: -6x + 6x = 0 -60 + 28x + -1x2 = 0 + x2 + -1x2 -60 + 28x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -60 + 28x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 60 + -28x + x2 = 0 Move the constant term to the right: Add '-60' to each side of the equation. 60 + -28x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + -28x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -28x + x2 = 0 + -60 -28x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 -28x + x2 = -60 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = -60 + 196 Reorder the terms: 196 + -28x + x2 = -60 + 196 Combine like terms: -60 + 196 = 136 196 + -28x + x2 = 136 Factor a perfect square on the left side: (x + -14)(x + -14) = 136 Calculate the square root of the right side: 11.66190379 Break this problem into two subproblems by setting (x + -14) equal to 11.66190379 and -11.66190379.Subproblem 1
x + -14 = 11.66190379 Simplifying x + -14 = 11.66190379 Reorder the terms: -14 + x = 11.66190379 Solving -14 + x = 11.66190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 11.66190379 + 14 Combine like terms: -14 + 14 = 0 0 + x = 11.66190379 + 14 x = 11.66190379 + 14 Combine like terms: 11.66190379 + 14 = 25.66190379 x = 25.66190379 Simplifying x = 25.66190379Subproblem 2
x + -14 = -11.66190379 Simplifying x + -14 = -11.66190379 Reorder the terms: -14 + x = -11.66190379 Solving -14 + x = -11.66190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -11.66190379 + 14 Combine like terms: -14 + 14 = 0 0 + x = -11.66190379 + 14 x = -11.66190379 + 14 Combine like terms: -11.66190379 + 14 = 2.33809621 x = 2.33809621 Simplifying x = 2.33809621Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.66190379, 2.33809621}
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