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Simplifying 64x2 + -128x = 25 Reorder the terms: -128x + 64x2 = 25 Solving -128x + 64x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + -128x + 64x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -128x + 64x2 = 0 Begin completing the square. Divide all terms by 64 the coefficient of the squared term: Divide each side by '64'. -0.390625 + -2x + x2 = 0 Move the constant term to the right: Add '0.390625' to each side of the equation. -0.390625 + -2x + 0.390625 + x2 = 0 + 0.390625 Reorder the terms: -0.390625 + 0.390625 + -2x + x2 = 0 + 0.390625 Combine like terms: -0.390625 + 0.390625 = 0.000000 0.000000 + -2x + x2 = 0 + 0.390625 -2x + x2 = 0 + 0.390625 Combine like terms: 0 + 0.390625 = 0.390625 -2x + x2 = 0.390625 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.390625 + 1 Reorder the terms: 1 + -2x + x2 = 0.390625 + 1 Combine like terms: 0.390625 + 1 = 1.390625 1 + -2x + x2 = 1.390625 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.390625 Calculate the square root of the right side: 1.179247642 Break this problem into two subproblems by setting (x + -1) equal to 1.179247642 and -1.179247642.Subproblem 1
x + -1 = 1.179247642 Simplifying x + -1 = 1.179247642 Reorder the terms: -1 + x = 1.179247642 Solving -1 + x = 1.179247642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.179247642 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.179247642 + 1 x = 1.179247642 + 1 Combine like terms: 1.179247642 + 1 = 2.179247642 x = 2.179247642 Simplifying x = 2.179247642Subproblem 2
x + -1 = -1.179247642 Simplifying x + -1 = -1.179247642 Reorder the terms: -1 + x = -1.179247642 Solving -1 + x = -1.179247642 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.179247642 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.179247642 + 1 x = -1.179247642 + 1 Combine like terms: -1.179247642 + 1 = -0.179247642 x = -0.179247642 Simplifying x = -0.179247642Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.179247642, -0.179247642}
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