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Simplifying 25x2 + -60x + 9 + -44x + -11 = 1 Reorder the terms: 9 + -11 + -60x + -44x + 25x2 = 1 Combine like terms: 9 + -11 = -2 -2 + -60x + -44x + 25x2 = 1 Combine like terms: -60x + -44x = -104x -2 + -104x + 25x2 = 1 Solving -2 + -104x + 25x2 = 1 Solving for variable 'x'. Reorder the terms: -2 + -1 + -104x + 25x2 = 1 + -1 Combine like terms: -2 + -1 = -3 -3 + -104x + 25x2 = 1 + -1 Combine like terms: 1 + -1 = 0 -3 + -104x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.12 + -4.16x + x2 = 0 Move the constant term to the right: Add '0.12' to each side of the equation. -0.12 + -4.16x + 0.12 + x2 = 0 + 0.12 Reorder the terms: -0.12 + 0.12 + -4.16x + x2 = 0 + 0.12 Combine like terms: -0.12 + 0.12 = 0.00 0.00 + -4.16x + x2 = 0 + 0.12 -4.16x + x2 = 0 + 0.12 Combine like terms: 0 + 0.12 = 0.12 -4.16x + x2 = 0.12 The x term is -4.16x. Take half its coefficient (-2.08). Square it (4.3264) and add it to both sides. Add '4.3264' to each side of the equation. -4.16x + 4.3264 + x2 = 0.12 + 4.3264 Reorder the terms: 4.3264 + -4.16x + x2 = 0.12 + 4.3264 Combine like terms: 0.12 + 4.3264 = 4.4464 4.3264 + -4.16x + x2 = 4.4464 Factor a perfect square on the left side: (x + -2.08)(x + -2.08) = 4.4464 Calculate the square root of the right side: 2.108648856 Break this problem into two subproblems by setting (x + -2.08) equal to 2.108648856 and -2.108648856.Subproblem 1
x + -2.08 = 2.108648856 Simplifying x + -2.08 = 2.108648856 Reorder the terms: -2.08 + x = 2.108648856 Solving -2.08 + x = 2.108648856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.08' to each side of the equation. -2.08 + 2.08 + x = 2.108648856 + 2.08 Combine like terms: -2.08 + 2.08 = 0.00 0.00 + x = 2.108648856 + 2.08 x = 2.108648856 + 2.08 Combine like terms: 2.108648856 + 2.08 = 4.188648856 x = 4.188648856 Simplifying x = 4.188648856Subproblem 2
x + -2.08 = -2.108648856 Simplifying x + -2.08 = -2.108648856 Reorder the terms: -2.08 + x = -2.108648856 Solving -2.08 + x = -2.108648856 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.08' to each side of the equation. -2.08 + 2.08 + x = -2.108648856 + 2.08 Combine like terms: -2.08 + 2.08 = 0.00 0.00 + x = -2.108648856 + 2.08 x = -2.108648856 + 2.08 Combine like terms: -2.108648856 + 2.08 = -0.028648856 x = -0.028648856 Simplifying x = -0.028648856Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.188648856, -0.028648856}
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