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Simplifying -1.75 = -4.9x2 + 12x Reorder the terms: -1.75 = 12x + -4.9x2 Solving -1.75 = 12x + -4.9x2 Solving for variable 'x'. Reorder the terms: -1.75 + -12x + 4.9x2 = 12x + -12x + -4.9x2 + 4.9x2 Combine like terms: 12x + -12x = 0 -1.75 + -12x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -1.75 + -12x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -1.75 + -12x + 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'. -0.3571428571 + -2.448979592x + x2 = 0 Move the constant term to the right: Add '0.3571428571' to each side of the equation. -0.3571428571 + -2.448979592x + 0.3571428571 + x2 = 0 + 0.3571428571 Reorder the terms: -0.3571428571 + 0.3571428571 + -2.448979592x + x2 = 0 + 0.3571428571 Combine like terms: -0.3571428571 + 0.3571428571 = 0.0000000000 0.0000000000 + -2.448979592x + x2 = 0 + 0.3571428571 -2.448979592x + x2 = 0 + 0.3571428571 Combine like terms: 0 + 0.3571428571 = 0.3571428571 -2.448979592x + x2 = 0.3571428571 The x term is -2.448979592x. Take half its coefficient (-1.224489796). Square it (1.499375261) and add it to both sides. Add '1.499375261' to each side of the equation. -2.448979592x + 1.499375261 + x2 = 0.3571428571 + 1.499375261 Reorder the terms: 1.499375261 + -2.448979592x + x2 = 0.3571428571 + 1.499375261 Combine like terms: 0.3571428571 + 1.499375261 = 1.8565181181 1.499375261 + -2.448979592x + x2 = 1.8565181181 Factor a perfect square on the left side: (x + -1.224489796)(x + -1.224489796) = 1.8565181181 Calculate the square root of the right side: 1.362541052 Break this problem into two subproblems by setting (x + -1.224489796) equal to 1.362541052 and -1.362541052.Subproblem 1
x + -1.224489796 = 1.362541052 Simplifying x + -1.224489796 = 1.362541052 Reorder the terms: -1.224489796 + x = 1.362541052 Solving -1.224489796 + x = 1.362541052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + x = 1.362541052 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + x = 1.362541052 + 1.224489796 x = 1.362541052 + 1.224489796 Combine like terms: 1.362541052 + 1.224489796 = 2.587030848 x = 2.587030848 Simplifying x = 2.587030848Subproblem 2
x + -1.224489796 = -1.362541052 Simplifying x + -1.224489796 = -1.362541052 Reorder the terms: -1.224489796 + x = -1.362541052 Solving -1.224489796 + x = -1.362541052 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.224489796' to each side of the equation. -1.224489796 + 1.224489796 + x = -1.362541052 + 1.224489796 Combine like terms: -1.224489796 + 1.224489796 = 0.000000000 0.000000000 + x = -1.362541052 + 1.224489796 x = -1.362541052 + 1.224489796 Combine like terms: -1.362541052 + 1.224489796 = -0.138051256 x = -0.138051256 Simplifying x = -0.138051256Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.587030848, -0.138051256}
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