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Simplifying 60(x) = 60 + -4.9x2 Solving 60x = 60 + -4.9x2 Solving for variable 'x'. Reorder the terms: -60 + 60x + 4.9x2 = 60 + -4.9x2 + -60 + 4.9x2 Reorder the terms: -60 + 60x + 4.9x2 = 60 + -60 + -4.9x2 + 4.9x2 Combine like terms: 60 + -60 = 0 -60 + 60x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -60 + 60x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -60 + 60x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -12.24489796 + 12.24489796x + x2 = 0 Move the constant term to the right: Add '12.24489796' to each side of the equation. -12.24489796 + 12.24489796x + 12.24489796 + x2 = 0 + 12.24489796 Reorder the terms: -12.24489796 + 12.24489796 + 12.24489796x + x2 = 0 + 12.24489796 Combine like terms: -12.24489796 + 12.24489796 = 0.00000000 0.00000000 + 12.24489796x + x2 = 0 + 12.24489796 12.24489796x + x2 = 0 + 12.24489796 Combine like terms: 0 + 12.24489796 = 12.24489796 12.24489796x + x2 = 12.24489796 The x term is 12.24489796x. Take half its coefficient (6.12244898). Square it (37.48438151) and add it to both sides. Add '37.48438151' to each side of the equation. 12.24489796x + 37.48438151 + x2 = 12.24489796 + 37.48438151 Reorder the terms: 37.48438151 + 12.24489796x + x2 = 12.24489796 + 37.48438151 Combine like terms: 12.24489796 + 37.48438151 = 49.72927947 37.48438151 + 12.24489796x + x2 = 49.72927947 Factor a perfect square on the left side: (x + 6.12244898)(x + 6.12244898) = 49.72927947 Calculate the square root of the right side: 7.051898997 Break this problem into two subproblems by setting (x + 6.12244898) equal to 7.051898997 and -7.051898997.Subproblem 1
x + 6.12244898 = 7.051898997 Simplifying x + 6.12244898 = 7.051898997 Reorder the terms: 6.12244898 + x = 7.051898997 Solving 6.12244898 + x = 7.051898997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.12244898' to each side of the equation. 6.12244898 + -6.12244898 + x = 7.051898997 + -6.12244898 Combine like terms: 6.12244898 + -6.12244898 = 0.00000000 0.00000000 + x = 7.051898997 + -6.12244898 x = 7.051898997 + -6.12244898 Combine like terms: 7.051898997 + -6.12244898 = 0.929450017 x = 0.929450017 Simplifying x = 0.929450017Subproblem 2
x + 6.12244898 = -7.051898997 Simplifying x + 6.12244898 = -7.051898997 Reorder the terms: 6.12244898 + x = -7.051898997 Solving 6.12244898 + x = -7.051898997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.12244898' to each side of the equation. 6.12244898 + -6.12244898 + x = -7.051898997 + -6.12244898 Combine like terms: 6.12244898 + -6.12244898 = 0.00000000 0.00000000 + x = -7.051898997 + -6.12244898 x = -7.051898997 + -6.12244898 Combine like terms: -7.051898997 + -6.12244898 = -13.174347977 x = -13.174347977 Simplifying x = -13.174347977Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.929450017, -13.174347977}
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