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Simplifying 25x2 + -64x + -1 = 0 Reorder the terms: -1 + -64x + 25x2 = 0 Solving -1 + -64x + 25x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. -0.04 + -2.56x + x2 = 0 Move the constant term to the right: Add '0.04' to each side of the equation. -0.04 + -2.56x + 0.04 + x2 = 0 + 0.04 Reorder the terms: -0.04 + 0.04 + -2.56x + x2 = 0 + 0.04 Combine like terms: -0.04 + 0.04 = 0.00 0.00 + -2.56x + x2 = 0 + 0.04 -2.56x + x2 = 0 + 0.04 Combine like terms: 0 + 0.04 = 0.04 -2.56x + x2 = 0.04 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 = 0.04 + 1.6384 Reorder the terms: 1.6384 + -2.56x + x2 = 0.04 + 1.6384 Combine like terms: 0.04 + 1.6384 = 1.6784 1.6384 + -2.56x + x2 = 1.6784 Factor a perfect square on the left side: (x + -1.28)(x + -1.28) = 1.6784 Calculate the square root of the right side: 1.295530779 Break this problem into two subproblems by setting (x + -1.28) equal to 1.295530779 and -1.295530779.Subproblem 1
x + -1.28 = 1.295530779 Simplifying x + -1.28 = 1.295530779 Reorder the terms: -1.28 + x = 1.295530779 Solving -1.28 + x = 1.295530779 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 = 1.295530779 + 1.28 Combine like terms: -1.28 + 1.28 = 0.00 0.00 + x = 1.295530779 + 1.28 x = 1.295530779 + 1.28 Combine like terms: 1.295530779 + 1.28 = 2.575530779 x = 2.575530779 Simplifying x = 2.575530779Subproblem 2
x + -1.28 = -1.295530779 Simplifying x + -1.28 = -1.295530779 Reorder the terms: -1.28 + x = -1.295530779 Solving -1.28 + x = -1.295530779 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 = -1.295530779 + 1.28 Combine like terms: -1.28 + 1.28 = 0.00 0.00 + x = -1.295530779 + 1.28 x = -1.295530779 + 1.28 Combine like terms: -1.295530779 + 1.28 = -0.015530779 x = -0.015530779 Simplifying x = -0.015530779Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.575530779, -0.015530779}
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