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Simplifying 25x2 + -16x + -8 = 0 Reorder the terms: -8 + -16x + 25x2 = 0 Solving -8 + -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'. -0.32 + -0.64x + x2 = 0 Move the constant term to the right: Add '0.32' to each side of the equation. -0.32 + -0.64x + 0.32 + x2 = 0 + 0.32 Reorder the terms: -0.32 + 0.32 + -0.64x + x2 = 0 + 0.32 Combine like terms: -0.32 + 0.32 = 0.00 0.00 + -0.64x + x2 = 0 + 0.32 -0.64x + x2 = 0 + 0.32 Combine like terms: 0 + 0.32 = 0.32 -0.64x + x2 = 0.32 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 = 0.32 + 0.1024 Reorder the terms: 0.1024 + -0.64x + x2 = 0.32 + 0.1024 Combine like terms: 0.32 + 0.1024 = 0.4224 0.1024 + -0.64x + x2 = 0.4224 Factor a perfect square on the left side: (x + -0.32)(x + -0.32) = 0.4224 Calculate the square root of the right side: 0.649923072 Break this problem into two subproblems by setting (x + -0.32) equal to 0.649923072 and -0.649923072.Subproblem 1
x + -0.32 = 0.649923072 Simplifying x + -0.32 = 0.649923072 Reorder the terms: -0.32 + x = 0.649923072 Solving -0.32 + x = 0.649923072 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 = 0.649923072 + 0.32 Combine like terms: -0.32 + 0.32 = 0.00 0.00 + x = 0.649923072 + 0.32 x = 0.649923072 + 0.32 Combine like terms: 0.649923072 + 0.32 = 0.969923072 x = 0.969923072 Simplifying x = 0.969923072Subproblem 2
x + -0.32 = -0.649923072 Simplifying x + -0.32 = -0.649923072 Reorder the terms: -0.32 + x = -0.649923072 Solving -0.32 + x = -0.649923072 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 = -0.649923072 + 0.32 Combine like terms: -0.32 + 0.32 = 0.00 0.00 + x = -0.649923072 + 0.32 x = -0.649923072 + 0.32 Combine like terms: -0.649923072 + 0.32 = -0.329923072 x = -0.329923072 Simplifying x = -0.329923072Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.969923072, -0.329923072}
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