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Simplifying x2 + -20x + -225 = 0 Reorder the terms: -225 + -20x + x2 = 0 Solving -225 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '225' to each side of the equation. -225 + -20x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + -20x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + -20x + x2 = 0 + 225 -20x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 -20x + x2 = 225 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 = 225 + 100 Reorder the terms: 100 + -20x + x2 = 225 + 100 Combine like terms: 225 + 100 = 325 100 + -20x + x2 = 325 Factor a perfect square on the left side: (x + -10)(x + -10) = 325 Calculate the square root of the right side: 18.027756377 Break this problem into two subproblems by setting (x + -10) equal to 18.027756377 and -18.027756377.Subproblem 1
x + -10 = 18.027756377 Simplifying x + -10 = 18.027756377 Reorder the terms: -10 + x = 18.027756377 Solving -10 + x = 18.027756377 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 = 18.027756377 + 10 Combine like terms: -10 + 10 = 0 0 + x = 18.027756377 + 10 x = 18.027756377 + 10 Combine like terms: 18.027756377 + 10 = 28.027756377 x = 28.027756377 Simplifying x = 28.027756377Subproblem 2
x + -10 = -18.027756377 Simplifying x + -10 = -18.027756377 Reorder the terms: -10 + x = -18.027756377 Solving -10 + x = -18.027756377 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 = -18.027756377 + 10 Combine like terms: -10 + 10 = 0 0 + x = -18.027756377 + 10 x = -18.027756377 + 10 Combine like terms: -18.027756377 + 10 = -8.027756377 x = -8.027756377 Simplifying x = -8.027756377Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.027756377, -8.027756377}
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