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Simplifying 16x2 + -20x + -20x + -25 = 64 Reorder the terms: -25 + -20x + -20x + 16x2 = 64 Combine like terms: -20x + -20x = -40x -25 + -40x + 16x2 = 64 Solving -25 + -40x + 16x2 = 64 Solving for variable 'x'. Reorder the terms: -25 + -64 + -40x + 16x2 = 64 + -64 Combine like terms: -25 + -64 = -89 -89 + -40x + 16x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -89 + -40x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -5.5625 + -2.5x + x2 = 0 Move the constant term to the right: Add '5.5625' to each side of the equation. -5.5625 + -2.5x + 5.5625 + x2 = 0 + 5.5625 Reorder the terms: -5.5625 + 5.5625 + -2.5x + x2 = 0 + 5.5625 Combine like terms: -5.5625 + 5.5625 = 0.0000 0.0000 + -2.5x + x2 = 0 + 5.5625 -2.5x + x2 = 0 + 5.5625 Combine like terms: 0 + 5.5625 = 5.5625 -2.5x + x2 = 5.5625 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 5.5625 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 5.5625 + 1.5625 Combine like terms: 5.5625 + 1.5625 = 7.125 1.5625 + -2.5x + x2 = 7.125 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 7.125 Calculate the square root of the right side: 2.669269563 Break this problem into two subproblems by setting (x + -1.25) equal to 2.669269563 and -2.669269563.Subproblem 1
x + -1.25 = 2.669269563 Simplifying x + -1.25 = 2.669269563 Reorder the terms: -1.25 + x = 2.669269563 Solving -1.25 + x = 2.669269563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.669269563 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.669269563 + 1.25 x = 2.669269563 + 1.25 Combine like terms: 2.669269563 + 1.25 = 3.919269563 x = 3.919269563 Simplifying x = 3.919269563Subproblem 2
x + -1.25 = -2.669269563 Simplifying x + -1.25 = -2.669269563 Reorder the terms: -1.25 + x = -2.669269563 Solving -1.25 + x = -2.669269563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.669269563 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.669269563 + 1.25 x = -2.669269563 + 1.25 Combine like terms: -2.669269563 + 1.25 = -1.419269563 x = -1.419269563 Simplifying x = -1.419269563Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.919269563, -1.419269563}
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