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Simplifying x2 + -20x + -3200 = 0 Reorder the terms: -3200 + -20x + x2 = 0 Solving -3200 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3200' to each side of the equation. -3200 + -20x + 3200 + x2 = 0 + 3200 Reorder the terms: -3200 + 3200 + -20x + x2 = 0 + 3200 Combine like terms: -3200 + 3200 = 0 0 + -20x + x2 = 0 + 3200 -20x + x2 = 0 + 3200 Combine like terms: 0 + 3200 = 3200 -20x + x2 = 3200 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 = 3200 + 100 Reorder the terms: 100 + -20x + x2 = 3200 + 100 Combine like terms: 3200 + 100 = 3300 100 + -20x + x2 = 3300 Factor a perfect square on the left side: (x + -10)(x + -10) = 3300 Calculate the square root of the right side: 57.445626465 Break this problem into two subproblems by setting (x + -10) equal to 57.445626465 and -57.445626465.Subproblem 1
x + -10 = 57.445626465 Simplifying x + -10 = 57.445626465 Reorder the terms: -10 + x = 57.445626465 Solving -10 + x = 57.445626465 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 = 57.445626465 + 10 Combine like terms: -10 + 10 = 0 0 + x = 57.445626465 + 10 x = 57.445626465 + 10 Combine like terms: 57.445626465 + 10 = 67.445626465 x = 67.445626465 Simplifying x = 67.445626465Subproblem 2
x + -10 = -57.445626465 Simplifying x + -10 = -57.445626465 Reorder the terms: -10 + x = -57.445626465 Solving -10 + x = -57.445626465 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 = -57.445626465 + 10 Combine like terms: -10 + 10 = 0 0 + x = -57.445626465 + 10 x = -57.445626465 + 10 Combine like terms: -57.445626465 + 10 = -47.445626465 x = -47.445626465 Simplifying x = -47.445626465Solution
The solution to the problem is based on the solutions from the subproblems. x = {67.445626465, -47.445626465}
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