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Simplifying 4x(4x + -1) = 5 Reorder the terms: 4x(-1 + 4x) = 5 (-1 * 4x + 4x * 4x) = 5 (-4x + 16x2) = 5 Solving -4x + 16x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + -4x + 16x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -4x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.3125 + -0.25x + x2 = 0 Move the constant term to the right: Add '0.3125' to each side of the equation. -0.3125 + -0.25x + 0.3125 + x2 = 0 + 0.3125 Reorder the terms: -0.3125 + 0.3125 + -0.25x + x2 = 0 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + -0.25x + x2 = 0 + 0.3125 -0.25x + x2 = 0 + 0.3125 Combine like terms: 0 + 0.3125 = 0.3125 -0.25x + x2 = 0.3125 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.3125 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.3125 + 0.015625 Combine like terms: 0.3125 + 0.015625 = 0.328125 0.015625 + -0.25x + x2 = 0.328125 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.328125 Calculate the square root of the right side: 0.572821962 Break this problem into two subproblems by setting (x + -0.125) equal to 0.572821962 and -0.572821962.Subproblem 1
x + -0.125 = 0.572821962 Simplifying x + -0.125 = 0.572821962 Reorder the terms: -0.125 + x = 0.572821962 Solving -0.125 + x = 0.572821962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.572821962 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.572821962 + 0.125 x = 0.572821962 + 0.125 Combine like terms: 0.572821962 + 0.125 = 0.697821962 x = 0.697821962 Simplifying x = 0.697821962Subproblem 2
x + -0.125 = -0.572821962 Simplifying x + -0.125 = -0.572821962 Reorder the terms: -0.125 + x = -0.572821962 Solving -0.125 + x = -0.572821962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.572821962 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.572821962 + 0.125 x = -0.572821962 + 0.125 Combine like terms: -0.572821962 + 0.125 = -0.447821962 x = -0.447821962 Simplifying x = -0.447821962Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.697821962, -0.447821962}
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