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Simplifying x2 + 20x + -2825 = 0 Reorder the terms: -2825 + 20x + x2 = 0 Solving -2825 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2825' to each side of the equation. -2825 + 20x + 2825 + x2 = 0 + 2825 Reorder the terms: -2825 + 2825 + 20x + x2 = 0 + 2825 Combine like terms: -2825 + 2825 = 0 0 + 20x + x2 = 0 + 2825 20x + x2 = 0 + 2825 Combine like terms: 0 + 2825 = 2825 20x + x2 = 2825 The x term is 20x. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20x + 100 + x2 = 2825 + 100 Reorder the terms: 100 + 20x + x2 = 2825 + 100 Combine like terms: 2825 + 100 = 2925 100 + 20x + x2 = 2925 Factor a perfect square on the left side: (x + 10)(x + 10) = 2925 Calculate the square root of the right side: 54.083269132 Break this problem into two subproblems by setting (x + 10) equal to 54.083269132 and -54.083269132.Subproblem 1
x + 10 = 54.083269132 Simplifying x + 10 = 54.083269132 Reorder the terms: 10 + x = 54.083269132 Solving 10 + x = 54.083269132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = 54.083269132 + -10 Combine like terms: 10 + -10 = 0 0 + x = 54.083269132 + -10 x = 54.083269132 + -10 Combine like terms: 54.083269132 + -10 = 44.083269132 x = 44.083269132 Simplifying x = 44.083269132Subproblem 2
x + 10 = -54.083269132 Simplifying x + 10 = -54.083269132 Reorder the terms: 10 + x = -54.083269132 Solving 10 + x = -54.083269132 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + x = -54.083269132 + -10 Combine like terms: 10 + -10 = 0 0 + x = -54.083269132 + -10 x = -54.083269132 + -10 Combine like terms: -54.083269132 + -10 = -64.083269132 x = -64.083269132 Simplifying x = -64.083269132Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.083269132, -64.083269132}
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