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Simplifying 3566 = 25x2 + -64x + 32 Reorder the terms: 3566 = 32 + -64x + 25x2 Solving 3566 = 32 + -64x + 25x2 Solving for variable 'x'. Combine like terms: 3566 + -32 = 3534 3534 + 64x + -25x2 = 32 + -64x + 25x2 + -32 + 64x + -25x2 Reorder the terms: 3534 + 64x + -25x2 = 32 + -32 + -64x + 64x + 25x2 + -25x2 Combine like terms: 32 + -32 = 0 3534 + 64x + -25x2 = 0 + -64x + 64x + 25x2 + -25x2 3534 + 64x + -25x2 = -64x + 64x + 25x2 + -25x2 Combine like terms: -64x + 64x = 0 3534 + 64x + -25x2 = 0 + 25x2 + -25x2 3534 + 64x + -25x2 = 25x2 + -25x2 Combine like terms: 25x2 + -25x2 = 0 3534 + 64x + -25x2 = 0 Begin completing the square. Divide all terms by -25 the coefficient of the squared term: Divide each side by '-25'. -141.36 + -2.56x + x2 = 0 Move the constant term to the right: Add '141.36' to each side of the equation. -141.36 + -2.56x + 141.36 + x2 = 0 + 141.36 Reorder the terms: -141.36 + 141.36 + -2.56x + x2 = 0 + 141.36 Combine like terms: -141.36 + 141.36 = 0.00 0.00 + -2.56x + x2 = 0 + 141.36 -2.56x + x2 = 0 + 141.36 Combine like terms: 0 + 141.36 = 141.36 -2.56x + x2 = 141.36 The x term is -2.56x. Take half its coefficient (-1.28). Square it (1.6384) and add it to both sides. Add '1.6384' to each side of the equation. -2.56x + 1.6384 + x2 = 141.36 + 1.6384 Reorder the terms: 1.6384 + -2.56x + x2 = 141.36 + 1.6384 Combine like terms: 141.36 + 1.6384 = 142.9984 1.6384 + -2.56x + x2 = 142.9984 Factor a perfect square on the left side: (x + -1.28)(x + -1.28) = 142.9984 Calculate the square root of the right side: 11.958193844 Break this problem into two subproblems by setting (x + -1.28) equal to 11.958193844 and -11.958193844.Subproblem 1
x + -1.28 = 11.958193844 Simplifying x + -1.28 = 11.958193844 Reorder the terms: -1.28 + x = 11.958193844 Solving -1.28 + x = 11.958193844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.28' to each side of the equation. -1.28 + 1.28 + x = 11.958193844 + 1.28 Combine like terms: -1.28 + 1.28 = 0.00 0.00 + x = 11.958193844 + 1.28 x = 11.958193844 + 1.28 Combine like terms: 11.958193844 + 1.28 = 13.238193844 x = 13.238193844 Simplifying x = 13.238193844Subproblem 2
x + -1.28 = -11.958193844 Simplifying x + -1.28 = -11.958193844 Reorder the terms: -1.28 + x = -11.958193844 Solving -1.28 + x = -11.958193844 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.28' to each side of the equation. -1.28 + 1.28 + x = -11.958193844 + 1.28 Combine like terms: -1.28 + 1.28 = 0.00 0.00 + x = -11.958193844 + 1.28 x = -11.958193844 + 1.28 Combine like terms: -11.958193844 + 1.28 = -10.678193844 x = -10.678193844 Simplifying x = -10.678193844Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.238193844, -10.678193844}
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