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Simplifying -4.9x2 + -17.5x + 60 = 0 Reorder the terms: 60 + -17.5x + -4.9x2 = 0 Solving 60 + -17.5x + -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 + 3.571428571x + x2 = 0 Move the constant term to the right: Add '12.24489796' to each side of the equation. -12.24489796 + 3.571428571x + 12.24489796 + x2 = 0 + 12.24489796 Reorder the terms: -12.24489796 + 12.24489796 + 3.571428571x + x2 = 0 + 12.24489796 Combine like terms: -12.24489796 + 12.24489796 = 0.00000000 0.00000000 + 3.571428571x + x2 = 0 + 12.24489796 3.571428571x + x2 = 0 + 12.24489796 Combine like terms: 0 + 12.24489796 = 12.24489796 3.571428571x + x2 = 12.24489796 The x term is 3.571428571x. Take half its coefficient (1.785714286). Square it (3.188775511) and add it to both sides. Add '3.188775511' to each side of the equation. 3.571428571x + 3.188775511 + x2 = 12.24489796 + 3.188775511 Reorder the terms: 3.188775511 + 3.571428571x + x2 = 12.24489796 + 3.188775511 Combine like terms: 12.24489796 + 3.188775511 = 15.433673471 3.188775511 + 3.571428571x + x2 = 15.433673471 Factor a perfect square on the left side: (x + 1.785714286)(x + 1.785714286) = 15.433673471 Calculate the square root of the right side: 3.928571429 Break this problem into two subproblems by setting (x + 1.785714286) equal to 3.928571429 and -3.928571429.Subproblem 1
x + 1.785714286 = 3.928571429 Simplifying x + 1.785714286 = 3.928571429 Reorder the terms: 1.785714286 + x = 3.928571429 Solving 1.785714286 + x = 3.928571429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.785714286' to each side of the equation. 1.785714286 + -1.785714286 + x = 3.928571429 + -1.785714286 Combine like terms: 1.785714286 + -1.785714286 = 0.000000000 0.000000000 + x = 3.928571429 + -1.785714286 x = 3.928571429 + -1.785714286 Combine like terms: 3.928571429 + -1.785714286 = 2.142857143 x = 2.142857143 Simplifying x = 2.142857143Subproblem 2
x + 1.785714286 = -3.928571429 Simplifying x + 1.785714286 = -3.928571429 Reorder the terms: 1.785714286 + x = -3.928571429 Solving 1.785714286 + x = -3.928571429 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.785714286' to each side of the equation. 1.785714286 + -1.785714286 + x = -3.928571429 + -1.785714286 Combine like terms: 1.785714286 + -1.785714286 = 0.000000000 0.000000000 + x = -3.928571429 + -1.785714286 x = -3.928571429 + -1.785714286 Combine like terms: -3.928571429 + -1.785714286 = -5.714285715 x = -5.714285715 Simplifying x = -5.714285715Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.142857143, -5.714285715}
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