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Simplifying 81 = 9x + x2 Solving 81 = 9x + x2 Solving for variable 'x'. Reorder the terms: 81 + -9x + -1x2 = 9x + -9x + x2 + -1x2 Combine like terms: 9x + -9x = 0 81 + -9x + -1x2 = 0 + x2 + -1x2 81 + -9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 81 + -9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -81 + 9x + x2 = 0 Move the constant term to the right: Add '81' to each side of the equation. -81 + 9x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + 9x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 9x + x2 = 0 + 81 9x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 9x + x2 = 81 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 = 81 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 81 + 20.25 Combine like terms: 81 + 20.25 = 101.25 20.25 + 9x + x2 = 101.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 101.25 Calculate the square root of the right side: 10.062305899 Break this problem into two subproblems by setting (x + 4.5) equal to 10.062305899 and -10.062305899.Subproblem 1
x + 4.5 = 10.062305899 Simplifying x + 4.5 = 10.062305899 Reorder the terms: 4.5 + x = 10.062305899 Solving 4.5 + x = 10.062305899 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 = 10.062305899 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 10.062305899 + -4.5 x = 10.062305899 + -4.5 Combine like terms: 10.062305899 + -4.5 = 5.562305899 x = 5.562305899 Simplifying x = 5.562305899Subproblem 2
x + 4.5 = -10.062305899 Simplifying x + 4.5 = -10.062305899 Reorder the terms: 4.5 + x = -10.062305899 Solving 4.5 + x = -10.062305899 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 = -10.062305899 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -10.062305899 + -4.5 x = -10.062305899 + -4.5 Combine like terms: -10.062305899 + -4.5 = -14.562305899 x = -14.562305899 Simplifying x = -14.562305899Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.562305899, -14.562305899}
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