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Simplifying x2 + 6x = 206.25 Reorder the terms: 6x + x2 = 206.25 Solving 6x + x2 = 206.25 Solving for variable 'x'. Reorder the terms: -206.25 + 6x + x2 = 206.25 + -206.25 Combine like terms: 206.25 + -206.25 = 0.00 -206.25 + 6x + x2 = 0.00 Begin completing the square. Move the constant term to the right: Add '206.25' to each side of the equation. -206.25 + 6x + 206.25 + x2 = 0.00 + 206.25 Reorder the terms: -206.25 + 206.25 + 6x + x2 = 0.00 + 206.25 Combine like terms: -206.25 + 206.25 = 0.00 0.00 + 6x + x2 = 0.00 + 206.25 6x + x2 = 0.00 + 206.25 Combine like terms: 0.00 + 206.25 = 206.25 6x + x2 = 206.25 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 = 206.25 + 9 Reorder the terms: 9 + 6x + x2 = 206.25 + 9 Combine like terms: 206.25 + 9 = 215.25 9 + 6x + x2 = 215.25 Factor a perfect square on the left side: (x + 3)(x + 3) = 215.25 Calculate the square root of the right side: 14.671400751 Break this problem into two subproblems by setting (x + 3) equal to 14.671400751 and -14.671400751.Subproblem 1
x + 3 = 14.671400751 Simplifying x + 3 = 14.671400751 Reorder the terms: 3 + x = 14.671400751 Solving 3 + x = 14.671400751 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 = 14.671400751 + -3 Combine like terms: 3 + -3 = 0 0 + x = 14.671400751 + -3 x = 14.671400751 + -3 Combine like terms: 14.671400751 + -3 = 11.671400751 x = 11.671400751 Simplifying x = 11.671400751Subproblem 2
x + 3 = -14.671400751 Simplifying x + 3 = -14.671400751 Reorder the terms: 3 + x = -14.671400751 Solving 3 + x = -14.671400751 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 = -14.671400751 + -3 Combine like terms: 3 + -3 = 0 0 + x = -14.671400751 + -3 x = -14.671400751 + -3 Combine like terms: -14.671400751 + -3 = -17.671400751 x = -17.671400751 Simplifying x = -17.671400751Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.671400751, -17.671400751}
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