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Simplifying x2 + 6x = 81 Reorder the terms: 6x + x2 = 81 Solving 6x + x2 = 81 Solving for variable 'x'. Reorder the terms: -81 + 6x + x2 = 81 + -81 Combine like terms: 81 + -81 = 0 -81 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '81' to each side of the equation. -81 + 6x + 81 + x2 = 0 + 81 Reorder the terms: -81 + 81 + 6x + x2 = 0 + 81 Combine like terms: -81 + 81 = 0 0 + 6x + x2 = 0 + 81 6x + x2 = 0 + 81 Combine like terms: 0 + 81 = 81 6x + x2 = 81 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 81 + 9 Reorder the terms: 9 + 6x + x2 = 81 + 9 Combine like terms: 81 + 9 = 90 9 + 6x + x2 = 90 Factor a perfect square on the left side: (x + 3)(x + 3) = 90 Calculate the square root of the right side: 9.486832981 Break this problem into two subproblems by setting (x + 3) equal to 9.486832981 and -9.486832981.Subproblem 1
x + 3 = 9.486832981 Simplifying x + 3 = 9.486832981 Reorder the terms: 3 + x = 9.486832981 Solving 3 + x = 9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 9.486832981 + -3 Combine like terms: 3 + -3 = 0 0 + x = 9.486832981 + -3 x = 9.486832981 + -3 Combine like terms: 9.486832981 + -3 = 6.486832981 x = 6.486832981 Simplifying x = 6.486832981Subproblem 2
x + 3 = -9.486832981 Simplifying x + 3 = -9.486832981 Reorder the terms: 3 + x = -9.486832981 Solving 3 + x = -9.486832981 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -9.486832981 + -3 Combine like terms: 3 + -3 = 0 0 + x = -9.486832981 + -3 x = -9.486832981 + -3 Combine like terms: -9.486832981 + -3 = -12.486832981 x = -12.486832981 Simplifying x = -12.486832981Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.486832981, -12.486832981}
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