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Simplifying 0.155279503x2 + 22.5x + -15.52795031 = 0 Reorder the terms: -15.52795031 + 22.5x + 0.155279503x2 = 0 Solving -15.52795031 + 22.5x + 0.155279503x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.155279503 the coefficient of the squared term: Divide each side by '0.155279503'. -100.0000001 + 144.9000001x + x2 = 0 Move the constant term to the right: Add '100.0000001' to each side of the equation. -100.0000001 + 144.9000001x + 100.0000001 + x2 = 0 + 100.0000001 Reorder the terms: -100.0000001 + 100.0000001 + 144.9000001x + x2 = 0 + 100.0000001 Combine like terms: -100.0000001 + 100.0000001 = 0.0000000 0.0000000 + 144.9000001x + x2 = 0 + 100.0000001 144.9000001x + x2 = 0 + 100.0000001 Combine like terms: 0 + 100.0000001 = 100.0000001 144.9000001x + x2 = 100.0000001 The x term is 144.9000001x. Take half its coefficient (72.45000005). Square it (5249.002507) and add it to both sides. Add '5249.002507' to each side of the equation. 144.9000001x + 5249.002507 + x2 = 100.0000001 + 5249.002507 Reorder the terms: 5249.002507 + 144.9000001x + x2 = 100.0000001 + 5249.002507 Combine like terms: 100.0000001 + 5249.002507 = 5349.0025071 5249.002507 + 144.9000001x + x2 = 5349.0025071 Factor a perfect square on the left side: (x + 72.45000005)(x + 72.45000005) = 5349.0025071 Calculate the square root of the right side: 73.136875153 Break this problem into two subproblems by setting (x + 72.45000005) equal to 73.136875153 and -73.136875153.Subproblem 1
x + 72.45000005 = 73.136875153 Simplifying x + 72.45000005 = 73.136875153 Reorder the terms: 72.45000005 + x = 73.136875153 Solving 72.45000005 + x = 73.136875153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-72.45000005' to each side of the equation. 72.45000005 + -72.45000005 + x = 73.136875153 + -72.45000005 Combine like terms: 72.45000005 + -72.45000005 = 0.00000000 0.00000000 + x = 73.136875153 + -72.45000005 x = 73.136875153 + -72.45000005 Combine like terms: 73.136875153 + -72.45000005 = 0.686875103 x = 0.686875103 Simplifying x = 0.686875103Subproblem 2
x + 72.45000005 = -73.136875153 Simplifying x + 72.45000005 = -73.136875153 Reorder the terms: 72.45000005 + x = -73.136875153 Solving 72.45000005 + x = -73.136875153 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-72.45000005' to each side of the equation. 72.45000005 + -72.45000005 + x = -73.136875153 + -72.45000005 Combine like terms: 72.45000005 + -72.45000005 = 0.00000000 0.00000000 + x = -73.136875153 + -72.45000005 x = -73.136875153 + -72.45000005 Combine like terms: -73.136875153 + -72.45000005 = -145.586875203 x = -145.586875203 Simplifying x = -145.586875203Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.686875103, -145.586875203}
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