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Simplifying 25x2 + -80x = 64 Reorder the terms: -80x + 25x2 = 64 Solving -80x + 25x2 = 64 Solving for variable 'x'. Reorder the terms: -64 + -80x + 25x2 = 64 + -64 Combine like terms: 64 + -64 = 0 -64 + -80x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -2.56 + -3.2x + x2 = 0 Move the constant term to the right: Add '2.56' to each side of the equation. -2.56 + -3.2x + 2.56 + x2 = 0 + 2.56 Reorder the terms: -2.56 + 2.56 + -3.2x + x2 = 0 + 2.56 Combine like terms: -2.56 + 2.56 = 0.00 0.00 + -3.2x + x2 = 0 + 2.56 -3.2x + x2 = 0 + 2.56 Combine like terms: 0 + 2.56 = 2.56 -3.2x + x2 = 2.56 The x term is -3.2x. Take half its coefficient (-1.6). Square it (2.56) and add it to both sides. Add '2.56' to each side of the equation. -3.2x + 2.56 + x2 = 2.56 + 2.56 Reorder the terms: 2.56 + -3.2x + x2 = 2.56 + 2.56 Combine like terms: 2.56 + 2.56 = 5.12 2.56 + -3.2x + x2 = 5.12 Factor a perfect square on the left side: (x + -1.6)(x + -1.6) = 5.12 Calculate the square root of the right side: 2.2627417 Break this problem into two subproblems by setting (x + -1.6) equal to 2.2627417 and -2.2627417.Subproblem 1
x + -1.6 = 2.2627417 Simplifying x + -1.6 = 2.2627417 Reorder the terms: -1.6 + x = 2.2627417 Solving -1.6 + x = 2.2627417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = 2.2627417 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = 2.2627417 + 1.6 x = 2.2627417 + 1.6 Combine like terms: 2.2627417 + 1.6 = 3.8627417 x = 3.8627417 Simplifying x = 3.8627417Subproblem 2
x + -1.6 = -2.2627417 Simplifying x + -1.6 = -2.2627417 Reorder the terms: -1.6 + x = -2.2627417 Solving -1.6 + x = -2.2627417 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + x = -2.2627417 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + x = -2.2627417 + 1.6 x = -2.2627417 + 1.6 Combine like terms: -2.2627417 + 1.6 = -0.6627417 x = -0.6627417 Simplifying x = -0.6627417Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.8627417, -0.6627417}
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