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Simplifying 25x2 = -11x + 17 Reorder the terms: 25x2 = 17 + -11x Solving 25x2 = 17 + -11x Solving for variable 'x'. Reorder the terms: -17 + 11x + 25x2 = 17 + -11x + -17 + 11x Reorder the terms: -17 + 11x + 25x2 = 17 + -17 + -11x + 11x Combine like terms: 17 + -17 = 0 -17 + 11x + 25x2 = 0 + -11x + 11x -17 + 11x + 25x2 = -11x + 11x Combine like terms: -11x + 11x = 0 -17 + 11x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.68 + 0.44x + x2 = 0 Move the constant term to the right: Add '0.68' to each side of the equation. -0.68 + 0.44x + 0.68 + x2 = 0 + 0.68 Reorder the terms: -0.68 + 0.68 + 0.44x + x2 = 0 + 0.68 Combine like terms: -0.68 + 0.68 = 0.00 0.00 + 0.44x + x2 = 0 + 0.68 0.44x + x2 = 0 + 0.68 Combine like terms: 0 + 0.68 = 0.68 0.44x + x2 = 0.68 The x term is 0.44x. Take half its coefficient (0.22). Square it (0.0484) and add it to both sides. Add '0.0484' to each side of the equation. 0.44x + 0.0484 + x2 = 0.68 + 0.0484 Reorder the terms: 0.0484 + 0.44x + x2 = 0.68 + 0.0484 Combine like terms: 0.68 + 0.0484 = 0.7284 0.0484 + 0.44x + x2 = 0.7284 Factor a perfect square on the left side: (x + 0.22)(x + 0.22) = 0.7284 Calculate the square root of the right side: 0.853463532 Break this problem into two subproblems by setting (x + 0.22) equal to 0.853463532 and -0.853463532.Subproblem 1
x + 0.22 = 0.853463532 Simplifying x + 0.22 = 0.853463532 Reorder the terms: 0.22 + x = 0.853463532 Solving 0.22 + x = 0.853463532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.22' to each side of the equation. 0.22 + -0.22 + x = 0.853463532 + -0.22 Combine like terms: 0.22 + -0.22 = 0.00 0.00 + x = 0.853463532 + -0.22 x = 0.853463532 + -0.22 Combine like terms: 0.853463532 + -0.22 = 0.633463532 x = 0.633463532 Simplifying x = 0.633463532Subproblem 2
x + 0.22 = -0.853463532 Simplifying x + 0.22 = -0.853463532 Reorder the terms: 0.22 + x = -0.853463532 Solving 0.22 + x = -0.853463532 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.22' to each side of the equation. 0.22 + -0.22 + x = -0.853463532 + -0.22 Combine like terms: 0.22 + -0.22 = 0.00 0.00 + x = -0.853463532 + -0.22 x = -0.853463532 + -0.22 Combine like terms: -0.853463532 + -0.22 = -1.073463532 x = -1.073463532 Simplifying x = -1.073463532Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.633463532, -1.073463532}
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