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Simplifying (2x + -5)(2x + -5) + (x + 4)(x + 4) = 41 Reorder the terms: (-5 + 2x)(2x + -5) + (x + 4)(x + 4) = 41 Reorder the terms: (-5 + 2x)(-5 + 2x) + (x + 4)(x + 4) = 41 Multiply (-5 + 2x) * (-5 + 2x) (-5(-5 + 2x) + 2x * (-5 + 2x)) + (x + 4)(x + 4) = 41 ((-5 * -5 + 2x * -5) + 2x * (-5 + 2x)) + (x + 4)(x + 4) = 41 ((25 + -10x) + 2x * (-5 + 2x)) + (x + 4)(x + 4) = 41 (25 + -10x + (-5 * 2x + 2x * 2x)) + (x + 4)(x + 4) = 41 (25 + -10x + (-10x + 4x2)) + (x + 4)(x + 4) = 41 Combine like terms: -10x + -10x = -20x (25 + -20x + 4x2) + (x + 4)(x + 4) = 41 Reorder the terms: 25 + -20x + 4x2 + (4 + x)(x + 4) = 41 Reorder the terms: 25 + -20x + 4x2 + (4 + x)(4 + x) = 41 Multiply (4 + x) * (4 + x) 25 + -20x + 4x2 + (4(4 + x) + x(4 + x)) = 41 25 + -20x + 4x2 + ((4 * 4 + x * 4) + x(4 + x)) = 41 25 + -20x + 4x2 + ((16 + 4x) + x(4 + x)) = 41 25 + -20x + 4x2 + (16 + 4x + (4 * x + x * x)) = 41 25 + -20x + 4x2 + (16 + 4x + (4x + x2)) = 41 Combine like terms: 4x + 4x = 8x 25 + -20x + 4x2 + (16 + 8x + x2) = 41 Reorder the terms: 25 + 16 + -20x + 8x + 4x2 + x2 = 41 Combine like terms: 25 + 16 = 41 41 + -20x + 8x + 4x2 + x2 = 41 Combine like terms: -20x + 8x = -12x 41 + -12x + 4x2 + x2 = 41 Combine like terms: 4x2 + x2 = 5x2 41 + -12x + 5x2 = 41 Add '-41' to each side of the equation. 41 + -12x + -41 + 5x2 = 41 + -41 Reorder the terms: 41 + -41 + -12x + 5x2 = 41 + -41 Combine like terms: 41 + -41 = 0 0 + -12x + 5x2 = 41 + -41 -12x + 5x2 = 41 + -41 Combine like terms: 41 + -41 = 0 -12x + 5x2 = 0 Solving -12x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-12 + 5x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-12 + 5x)' equal to zero and attempt to solve: Simplifying -12 + 5x = 0 Solving -12 + 5x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + 5x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + 5x = 0 + 12 5x = 0 + 12 Combine like terms: 0 + 12 = 12 5x = 12 Divide each side by '5'. x = 2.4 Simplifying x = 2.4Solution
x = {0, 2.4}
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