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Simplifying 4x(x + -1) + -1(2x + 5)(2x + -5) = 1 Reorder the terms: 4x(-1 + x) + -1(2x + 5)(2x + -5) = 1 (-1 * 4x + x * 4x) + -1(2x + 5)(2x + -5) = 1 (-4x + 4x2) + -1(2x + 5)(2x + -5) = 1 Reorder the terms: -4x + 4x2 + -1(5 + 2x)(2x + -5) = 1 Reorder the terms: -4x + 4x2 + -1(5 + 2x)(-5 + 2x) = 1 Multiply (5 + 2x) * (-5 + 2x) -4x + 4x2 + -1(5(-5 + 2x) + 2x * (-5 + 2x)) = 1 -4x + 4x2 + -1((-5 * 5 + 2x * 5) + 2x * (-5 + 2x)) = 1 -4x + 4x2 + -1((-25 + 10x) + 2x * (-5 + 2x)) = 1 -4x + 4x2 + -1(-25 + 10x + (-5 * 2x + 2x * 2x)) = 1 -4x + 4x2 + -1(-25 + 10x + (-10x + 4x2)) = 1 Combine like terms: 10x + -10x = 0 -4x + 4x2 + -1(-25 + 0 + 4x2) = 1 -4x + 4x2 + -1(-25 + 4x2) = 1 -4x + 4x2 + (-25 * -1 + 4x2 * -1) = 1 -4x + 4x2 + (25 + -4x2) = 1 Reorder the terms: 25 + -4x + 4x2 + -4x2 = 1 Combine like terms: 4x2 + -4x2 = 0 25 + -4x + 0 = 1 25 + -4x = 1 Solving 25 + -4x = 1 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -4x = 1 + -25 Combine like terms: 25 + -25 = 0 0 + -4x = 1 + -25 -4x = 1 + -25 Combine like terms: 1 + -25 = -24 -4x = -24 Divide each side by '-4'. x = 6 Simplifying x = 6
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