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Simplifying 8x2 + -65x = -35 Reorder the terms: -65x + 8x2 = -35 Solving -65x + 8x2 = -35 Solving for variable 'x'. Reorder the terms: 35 + -65x + 8x2 = -35 + 35 Combine like terms: -35 + 35 = 0 35 + -65x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 4.375 + -8.125x + x2 = 0 Move the constant term to the right: Add '-4.375' to each side of the equation. 4.375 + -8.125x + -4.375 + x2 = 0 + -4.375 Reorder the terms: 4.375 + -4.375 + -8.125x + x2 = 0 + -4.375 Combine like terms: 4.375 + -4.375 = 0.000 0.000 + -8.125x + x2 = 0 + -4.375 -8.125x + x2 = 0 + -4.375 Combine like terms: 0 + -4.375 = -4.375 -8.125x + x2 = -4.375 The x term is -8.125x. Take half its coefficient (-4.0625). Square it (16.50390625) and add it to both sides. Add '16.50390625' to each side of the equation. -8.125x + 16.50390625 + x2 = -4.375 + 16.50390625 Reorder the terms: 16.50390625 + -8.125x + x2 = -4.375 + 16.50390625 Combine like terms: -4.375 + 16.50390625 = 12.12890625 16.50390625 + -8.125x + x2 = 12.12890625 Factor a perfect square on the left side: (x + -4.0625)(x + -4.0625) = 12.12890625 Calculate the square root of the right side: 3.482657929 Break this problem into two subproblems by setting (x + -4.0625) equal to 3.482657929 and -3.482657929.Subproblem 1
x + -4.0625 = 3.482657929 Simplifying x + -4.0625 = 3.482657929 Reorder the terms: -4.0625 + x = 3.482657929 Solving -4.0625 + x = 3.482657929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.0625' to each side of the equation. -4.0625 + 4.0625 + x = 3.482657929 + 4.0625 Combine like terms: -4.0625 + 4.0625 = 0.0000 0.0000 + x = 3.482657929 + 4.0625 x = 3.482657929 + 4.0625 Combine like terms: 3.482657929 + 4.0625 = 7.545157929 x = 7.545157929 Simplifying x = 7.545157929Subproblem 2
x + -4.0625 = -3.482657929 Simplifying x + -4.0625 = -3.482657929 Reorder the terms: -4.0625 + x = -3.482657929 Solving -4.0625 + x = -3.482657929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.0625' to each side of the equation. -4.0625 + 4.0625 + x = -3.482657929 + 4.0625 Combine like terms: -4.0625 + 4.0625 = 0.0000 0.0000 + x = -3.482657929 + 4.0625 x = -3.482657929 + 4.0625 Combine like terms: -3.482657929 + 4.0625 = 0.579842071 x = 0.579842071 Simplifying x = 0.579842071Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.545157929, 0.579842071}
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