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Simplifying x2 + 9 = 9x + 81 Reorder the terms: 9 + x2 = 9x + 81 Reorder the terms: 9 + x2 = 81 + 9x Solving 9 + x2 = 81 + 9x Solving for variable 'x'. Reorder the terms: 9 + -81 + -9x + x2 = 81 + 9x + -81 + -9x Combine like terms: 9 + -81 = -72 -72 + -9x + x2 = 81 + 9x + -81 + -9x Reorder the terms: -72 + -9x + x2 = 81 + -81 + 9x + -9x Combine like terms: 81 + -81 = 0 -72 + -9x + x2 = 0 + 9x + -9x -72 + -9x + x2 = 9x + -9x Combine like terms: 9x + -9x = 0 -72 + -9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '72' to each side of the equation. -72 + -9x + 72 + x2 = 0 + 72 Reorder the terms: -72 + 72 + -9x + x2 = 0 + 72 Combine like terms: -72 + 72 = 0 0 + -9x + x2 = 0 + 72 -9x + x2 = 0 + 72 Combine like terms: 0 + 72 = 72 -9x + x2 = 72 The x term is -9x. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9x + 20.25 + x2 = 72 + 20.25 Reorder the terms: 20.25 + -9x + x2 = 72 + 20.25 Combine like terms: 72 + 20.25 = 92.25 20.25 + -9x + x2 = 92.25 Factor a perfect square on the left side: (x + -4.5)(x + -4.5) = 92.25 Calculate the square root of the right side: 9.604686356 Break this problem into two subproblems by setting (x + -4.5) equal to 9.604686356 and -9.604686356.Subproblem 1
x + -4.5 = 9.604686356 Simplifying x + -4.5 = 9.604686356 Reorder the terms: -4.5 + x = 9.604686356 Solving -4.5 + x = 9.604686356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = 9.604686356 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = 9.604686356 + 4.5 x = 9.604686356 + 4.5 Combine like terms: 9.604686356 + 4.5 = 14.104686356 x = 14.104686356 Simplifying x = 14.104686356Subproblem 2
x + -4.5 = -9.604686356 Simplifying x + -4.5 = -9.604686356 Reorder the terms: -4.5 + x = -9.604686356 Solving -4.5 + x = -9.604686356 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + x = -9.604686356 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + x = -9.604686356 + 4.5 x = -9.604686356 + 4.5 Combine like terms: -9.604686356 + 4.5 = -5.104686356 x = -5.104686356 Simplifying x = -5.104686356Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.104686356, -5.104686356}
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