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Simplifying (4x + 1)(4x + 1) = (x + 10)(x + 10) Reorder the terms: (1 + 4x)(4x + 1) = (x + 10)(x + 10) Reorder the terms: (1 + 4x)(1 + 4x) = (x + 10)(x + 10) Multiply (1 + 4x) * (1 + 4x) (1(1 + 4x) + 4x * (1 + 4x)) = (x + 10)(x + 10) ((1 * 1 + 4x * 1) + 4x * (1 + 4x)) = (x + 10)(x + 10) ((1 + 4x) + 4x * (1 + 4x)) = (x + 10)(x + 10) (1 + 4x + (1 * 4x + 4x * 4x)) = (x + 10)(x + 10) (1 + 4x + (4x + 16x2)) = (x + 10)(x + 10) Combine like terms: 4x + 4x = 8x (1 + 8x + 16x2) = (x + 10)(x + 10) Reorder the terms: 1 + 8x + 16x2 = (10 + x)(x + 10) Reorder the terms: 1 + 8x + 16x2 = (10 + x)(10 + x) Multiply (10 + x) * (10 + x) 1 + 8x + 16x2 = (10(10 + x) + x(10 + x)) 1 + 8x + 16x2 = ((10 * 10 + x * 10) + x(10 + x)) 1 + 8x + 16x2 = ((100 + 10x) + x(10 + x)) 1 + 8x + 16x2 = (100 + 10x + (10 * x + x * x)) 1 + 8x + 16x2 = (100 + 10x + (10x + x2)) Combine like terms: 10x + 10x = 20x 1 + 8x + 16x2 = (100 + 20x + x2) Solving 1 + 8x + 16x2 = 100 + 20x + x2 Solving for variable 'x'. Reorder the terms: 1 + -100 + 8x + -20x + 16x2 + -1x2 = 100 + 20x + x2 + -100 + -20x + -1x2 Combine like terms: 1 + -100 = -99 -99 + 8x + -20x + 16x2 + -1x2 = 100 + 20x + x2 + -100 + -20x + -1x2 Combine like terms: 8x + -20x = -12x -99 + -12x + 16x2 + -1x2 = 100 + 20x + x2 + -100 + -20x + -1x2 Combine like terms: 16x2 + -1x2 = 15x2 -99 + -12x + 15x2 = 100 + 20x + x2 + -100 + -20x + -1x2 Reorder the terms: -99 + -12x + 15x2 = 100 + -100 + 20x + -20x + x2 + -1x2 Combine like terms: 100 + -100 = 0 -99 + -12x + 15x2 = 0 + 20x + -20x + x2 + -1x2 -99 + -12x + 15x2 = 20x + -20x + x2 + -1x2 Combine like terms: 20x + -20x = 0 -99 + -12x + 15x2 = 0 + x2 + -1x2 -99 + -12x + 15x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -99 + -12x + 15x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-33 + -4x + 5x2) = 0 Factor a trinomial. 3((-11 + -5x)(3 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-11 + -5x)' equal to zero and attempt to solve: Simplifying -11 + -5x = 0 Solving -11 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -5x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -5x = 0 + 11 -5x = 0 + 11 Combine like terms: 0 + 11 = 11 -5x = 11 Divide each side by '-5'. x = -2.2 Simplifying x = -2.2Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-2.2, 3}
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