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Simplifying 64x2 + -80x + 5 = 0 Reorder the terms: 5 + -80x + 64x2 = 0 Solving 5 + -80x + 64x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. 0.078125 + -1.25x + x2 = 0 Move the constant term to the right: Add '-0.078125' to each side of the equation. 0.078125 + -1.25x + -0.078125 + x2 = 0 + -0.078125 Reorder the terms: 0.078125 + -0.078125 + -1.25x + x2 = 0 + -0.078125 Combine like terms: 0.078125 + -0.078125 = 0.000000 0.000000 + -1.25x + x2 = 0 + -0.078125 -1.25x + x2 = 0 + -0.078125 Combine like terms: 0 + -0.078125 = -0.078125 -1.25x + x2 = -0.078125 The x term is -1.25x. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25x + 0.390625 + x2 = -0.078125 + 0.390625 Reorder the terms: 0.390625 + -1.25x + x2 = -0.078125 + 0.390625 Combine like terms: -0.078125 + 0.390625 = 0.3125 0.390625 + -1.25x + x2 = 0.3125 Factor a perfect square on the left side: (x + -0.625)(x + -0.625) = 0.3125 Calculate the square root of the right side: 0.559016994 Break this problem into two subproblems by setting (x + -0.625) equal to 0.559016994 and -0.559016994.Subproblem 1
x + -0.625 = 0.559016994 Simplifying x + -0.625 = 0.559016994 Reorder the terms: -0.625 + x = 0.559016994 Solving -0.625 + x = 0.559016994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = 0.559016994 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = 0.559016994 + 0.625 x = 0.559016994 + 0.625 Combine like terms: 0.559016994 + 0.625 = 1.184016994 x = 1.184016994 Simplifying x = 1.184016994Subproblem 2
x + -0.625 = -0.559016994 Simplifying x + -0.625 = -0.559016994 Reorder the terms: -0.625 + x = -0.559016994 Solving -0.625 + x = -0.559016994 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + x = -0.559016994 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + x = -0.559016994 + 0.625 x = -0.559016994 + 0.625 Combine like terms: -0.559016994 + 0.625 = 0.065983006 x = 0.065983006 Simplifying x = 0.065983006Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.184016994, 0.065983006}
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