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Simplifying 4x2 + -65x + 64 = 0 Reorder the terms: 64 + -65x + 4x2 = 0 Solving 64 + -65x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 16 + -16.25x + x2 = 0 Move the constant term to the right: Add '-16' to each side of the equation. 16 + -16.25x + -16 + x2 = 0 + -16 Reorder the terms: 16 + -16 + -16.25x + x2 = 0 + -16 Combine like terms: 16 + -16 = 0 0 + -16.25x + x2 = 0 + -16 -16.25x + x2 = 0 + -16 Combine like terms: 0 + -16 = -16 -16.25x + x2 = -16 The x term is -16.25x. Take half its coefficient (-8.125). Square it (66.015625) and add it to both sides. Add '66.015625' to each side of the equation. -16.25x + 66.015625 + x2 = -16 + 66.015625 Reorder the terms: 66.015625 + -16.25x + x2 = -16 + 66.015625 Combine like terms: -16 + 66.015625 = 50.015625 66.015625 + -16.25x + x2 = 50.015625 Factor a perfect square on the left side: (x + -8.125)(x + -8.125) = 50.015625 Calculate the square root of the right side: 7.07217258 Break this problem into two subproblems by setting (x + -8.125) equal to 7.07217258 and -7.07217258.Subproblem 1
x + -8.125 = 7.07217258 Simplifying x + -8.125 = 7.07217258 Reorder the terms: -8.125 + x = 7.07217258 Solving -8.125 + x = 7.07217258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.125' to each side of the equation. -8.125 + 8.125 + x = 7.07217258 + 8.125 Combine like terms: -8.125 + 8.125 = 0.000 0.000 + x = 7.07217258 + 8.125 x = 7.07217258 + 8.125 Combine like terms: 7.07217258 + 8.125 = 15.19717258 x = 15.19717258 Simplifying x = 15.19717258Subproblem 2
x + -8.125 = -7.07217258 Simplifying x + -8.125 = -7.07217258 Reorder the terms: -8.125 + x = -7.07217258 Solving -8.125 + x = -7.07217258 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.125' to each side of the equation. -8.125 + 8.125 + x = -7.07217258 + 8.125 Combine like terms: -8.125 + 8.125 = 0.000 0.000 + x = -7.07217258 + 8.125 x = -7.07217258 + 8.125 Combine like terms: -7.07217258 + 8.125 = 1.05282742 x = 1.05282742 Simplifying x = 1.05282742Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.19717258, 1.05282742}
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