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Simplifying x2 + 20x + -2475 = 0 Reorder the terms: -2475 + 20x + x2 = 0 Solving -2475 + 20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2475' to each side of the equation. -2475 + 20x + 2475 + x2 = 0 + 2475 Reorder the terms: -2475 + 2475 + 20x + x2 = 0 + 2475 Combine like terms: -2475 + 2475 = 0 0 + 20x + x2 = 0 + 2475 20x + x2 = 0 + 2475 Combine like terms: 0 + 2475 = 2475 20x + x2 = 2475 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 = 2475 + 100 Reorder the terms: 100 + 20x + x2 = 2475 + 100 Combine like terms: 2475 + 100 = 2575 100 + 20x + x2 = 2575 Factor a perfect square on the left side: (x + 10)(x + 10) = 2575 Calculate the square root of the right side: 50.744457825 Break this problem into two subproblems by setting (x + 10) equal to 50.744457825 and -50.744457825.Subproblem 1
x + 10 = 50.744457825 Simplifying x + 10 = 50.744457825 Reorder the terms: 10 + x = 50.744457825 Solving 10 + x = 50.744457825 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 = 50.744457825 + -10 Combine like terms: 10 + -10 = 0 0 + x = 50.744457825 + -10 x = 50.744457825 + -10 Combine like terms: 50.744457825 + -10 = 40.744457825 x = 40.744457825 Simplifying x = 40.744457825Subproblem 2
x + 10 = -50.744457825 Simplifying x + 10 = -50.744457825 Reorder the terms: 10 + x = -50.744457825 Solving 10 + x = -50.744457825 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 = -50.744457825 + -10 Combine like terms: 10 + -10 = 0 0 + x = -50.744457825 + -10 x = -50.744457825 + -10 Combine like terms: -50.744457825 + -10 = -60.744457825 x = -60.744457825 Simplifying x = -60.744457825Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.744457825, -60.744457825}
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