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Simplifying 25x2 + -16x + -16 = 0 Reorder the terms: -16 + -16x + 25x2 = 0 Solving -16 + -16x + 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'. -0.64 + -0.64x + x2 = 0 Move the constant term to the right: Add '0.64' to each side of the equation. -0.64 + -0.64x + 0.64 + x2 = 0 + 0.64 Reorder the terms: -0.64 + 0.64 + -0.64x + x2 = 0 + 0.64 Combine like terms: -0.64 + 0.64 = 0.00 0.00 + -0.64x + x2 = 0 + 0.64 -0.64x + x2 = 0 + 0.64 Combine like terms: 0 + 0.64 = 0.64 -0.64x + x2 = 0.64 The x term is -0.64x. Take half its coefficient (-0.32). Square it (0.1024) and add it to both sides. Add '0.1024' to each side of the equation. -0.64x + 0.1024 + x2 = 0.64 + 0.1024 Reorder the terms: 0.1024 + -0.64x + x2 = 0.64 + 0.1024 Combine like terms: 0.64 + 0.1024 = 0.7424 0.1024 + -0.64x + x2 = 0.7424 Factor a perfect square on the left side: (x + -0.32)(x + -0.32) = 0.7424 Calculate the square root of the right side: 0.861626369 Break this problem into two subproblems by setting (x + -0.32) equal to 0.861626369 and -0.861626369.Subproblem 1
x + -0.32 = 0.861626369 Simplifying x + -0.32 = 0.861626369 Reorder the terms: -0.32 + x = 0.861626369 Solving -0.32 + x = 0.861626369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.32' to each side of the equation. -0.32 + 0.32 + x = 0.861626369 + 0.32 Combine like terms: -0.32 + 0.32 = 0.00 0.00 + x = 0.861626369 + 0.32 x = 0.861626369 + 0.32 Combine like terms: 0.861626369 + 0.32 = 1.181626369 x = 1.181626369 Simplifying x = 1.181626369Subproblem 2
x + -0.32 = -0.861626369 Simplifying x + -0.32 = -0.861626369 Reorder the terms: -0.32 + x = -0.861626369 Solving -0.32 + x = -0.861626369 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.32' to each side of the equation. -0.32 + 0.32 + x = -0.861626369 + 0.32 Combine like terms: -0.32 + 0.32 = 0.00 0.00 + x = -0.861626369 + 0.32 x = -0.861626369 + 0.32 Combine like terms: -0.861626369 + 0.32 = -0.541626369 x = -0.541626369 Simplifying x = -0.541626369Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.181626369, -0.541626369}
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