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Simplifying 4.9x2 + 6x + -60 = 0 Reorder the terms: -60 + 6x + 4.9x2 = 0 Solving -60 + 6x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -12.24489796 + 1.224489796x + x2 = 0 Move the constant term to the right: Add '12.24489796' to each side of the equation. -12.24489796 + 1.224489796x + 12.24489796 + x2 = 0 + 12.24489796 Reorder the terms: -12.24489796 + 12.24489796 + 1.224489796x + x2 = 0 + 12.24489796 Combine like terms: -12.24489796 + 12.24489796 = 0.00000000 0.00000000 + 1.224489796x + x2 = 0 + 12.24489796 1.224489796x + x2 = 0 + 12.24489796 Combine like terms: 0 + 12.24489796 = 12.24489796 1.224489796x + x2 = 12.24489796 The x term is 1.224489796x. Take half its coefficient (0.612244898). Square it (0.3748438151) and add it to both sides. Add '0.3748438151' to each side of the equation. 1.224489796x + 0.3748438151 + x2 = 12.24489796 + 0.3748438151 Reorder the terms: 0.3748438151 + 1.224489796x + x2 = 12.24489796 + 0.3748438151 Combine like terms: 12.24489796 + 0.3748438151 = 12.6197417751 0.3748438151 + 1.224489796x + x2 = 12.6197417751 Factor a perfect square on the left side: (x + 0.612244898)(x + 0.612244898) = 12.6197417751 Calculate the square root of the right side: 3.552427589 Break this problem into two subproblems by setting (x + 0.612244898) equal to 3.552427589 and -3.552427589.Subproblem 1
x + 0.612244898 = 3.552427589 Simplifying x + 0.612244898 = 3.552427589 Reorder the terms: 0.612244898 + x = 3.552427589 Solving 0.612244898 + x = 3.552427589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.612244898' to each side of the equation. 0.612244898 + -0.612244898 + x = 3.552427589 + -0.612244898 Combine like terms: 0.612244898 + -0.612244898 = 0.000000000 0.000000000 + x = 3.552427589 + -0.612244898 x = 3.552427589 + -0.612244898 Combine like terms: 3.552427589 + -0.612244898 = 2.940182691 x = 2.940182691 Simplifying x = 2.940182691Subproblem 2
x + 0.612244898 = -3.552427589 Simplifying x + 0.612244898 = -3.552427589 Reorder the terms: 0.612244898 + x = -3.552427589 Solving 0.612244898 + x = -3.552427589 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.612244898' to each side of the equation. 0.612244898 + -0.612244898 + x = -3.552427589 + -0.612244898 Combine like terms: 0.612244898 + -0.612244898 = 0.000000000 0.000000000 + x = -3.552427589 + -0.612244898 x = -3.552427589 + -0.612244898 Combine like terms: -3.552427589 + -0.612244898 = -4.164672487 x = -4.164672487 Simplifying x = -4.164672487Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.940182691, -4.164672487}
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