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Simplifying x2 + 30x + -2700 = 0 Reorder the terms: -2700 + 30x + x2 = 0 Solving -2700 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2700' to each side of the equation. -2700 + 30x + 2700 + x2 = 0 + 2700 Reorder the terms: -2700 + 2700 + 30x + x2 = 0 + 2700 Combine like terms: -2700 + 2700 = 0 0 + 30x + x2 = 0 + 2700 30x + x2 = 0 + 2700 Combine like terms: 0 + 2700 = 2700 30x + x2 = 2700 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 2700 + 225 Reorder the terms: 225 + 30x + x2 = 2700 + 225 Combine like terms: 2700 + 225 = 2925 225 + 30x + x2 = 2925 Factor a perfect square on the left side: (x + 15)(x + 15) = 2925 Calculate the square root of the right side: 54.083269132 Break this problem into two subproblems by setting (x + 15) equal to 54.083269132 and -54.083269132.Subproblem 1
x + 15 = 54.083269132 Simplifying x + 15 = 54.083269132 Reorder the terms: 15 + x = 54.083269132 Solving 15 + x = 54.083269132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 54.083269132 + -15 Combine like terms: 15 + -15 = 0 0 + x = 54.083269132 + -15 x = 54.083269132 + -15 Combine like terms: 54.083269132 + -15 = 39.083269132 x = 39.083269132 Simplifying x = 39.083269132Subproblem 2
x + 15 = -54.083269132 Simplifying x + 15 = -54.083269132 Reorder the terms: 15 + x = -54.083269132 Solving 15 + x = -54.083269132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -54.083269132 + -15 Combine like terms: 15 + -15 = 0 0 + x = -54.083269132 + -15 x = -54.083269132 + -15 Combine like terms: -54.083269132 + -15 = -69.083269132 x = -69.083269132 Simplifying x = -69.083269132Solution
The solution to the problem is based on the solutions from the subproblems. x = {39.083269132, -69.083269132}
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