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Simplifying x2 + -20x + -144 = 0 Reorder the terms: -144 + -20x + x2 = 0 Solving -144 + -20x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '144' to each side of the equation. -144 + -20x + 144 + x2 = 0 + 144 Reorder the terms: -144 + 144 + -20x + x2 = 0 + 144 Combine like terms: -144 + 144 = 0 0 + -20x + x2 = 0 + 144 -20x + x2 = 0 + 144 Combine like terms: 0 + 144 = 144 -20x + x2 = 144 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 = 144 + 100 Reorder the terms: 100 + -20x + x2 = 144 + 100 Combine like terms: 144 + 100 = 244 100 + -20x + x2 = 244 Factor a perfect square on the left side: (x + -10)(x + -10) = 244 Calculate the square root of the right side: 15.620499352 Break this problem into two subproblems by setting (x + -10) equal to 15.620499352 and -15.620499352.Subproblem 1
x + -10 = 15.620499352 Simplifying x + -10 = 15.620499352 Reorder the terms: -10 + x = 15.620499352 Solving -10 + x = 15.620499352 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 = 15.620499352 + 10 Combine like terms: -10 + 10 = 0 0 + x = 15.620499352 + 10 x = 15.620499352 + 10 Combine like terms: 15.620499352 + 10 = 25.620499352 x = 25.620499352 Simplifying x = 25.620499352Subproblem 2
x + -10 = -15.620499352 Simplifying x + -10 = -15.620499352 Reorder the terms: -10 + x = -15.620499352 Solving -10 + x = -15.620499352 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 = -15.620499352 + 10 Combine like terms: -10 + 10 = 0 0 + x = -15.620499352 + 10 x = -15.620499352 + 10 Combine like terms: -15.620499352 + 10 = -5.620499352 x = -5.620499352 Simplifying x = -5.620499352Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.620499352, -5.620499352}
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