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Simplifying (1 + -3x)(1 + 3x) + 10x2 = (x + -2)(x + -2) + 17 Multiply (1 + -3x) * (1 + 3x) (1(1 + 3x) + -3x * (1 + 3x)) + 10x2 = (x + -2)(x + -2) + 17 ((1 * 1 + 3x * 1) + -3x * (1 + 3x)) + 10x2 = (x + -2)(x + -2) + 17 ((1 + 3x) + -3x * (1 + 3x)) + 10x2 = (x + -2)(x + -2) + 17 (1 + 3x + (1 * -3x + 3x * -3x)) + 10x2 = (x + -2)(x + -2) + 17 (1 + 3x + (-3x + -9x2)) + 10x2 = (x + -2)(x + -2) + 17 Combine like terms: 3x + -3x = 0 (1 + 0 + -9x2) + 10x2 = (x + -2)(x + -2) + 17 (1 + -9x2) + 10x2 = (x + -2)(x + -2) + 17 Combine like terms: -9x2 + 10x2 = 1x2 1 + 1x2 = (x + -2)(x + -2) + 17 Reorder the terms: 1 + 1x2 = (-2 + x)(x + -2) + 17 Reorder the terms: 1 + 1x2 = (-2 + x)(-2 + x) + 17 Multiply (-2 + x) * (-2 + x) 1 + 1x2 = (-2(-2 + x) + x(-2 + x)) + 17 1 + 1x2 = ((-2 * -2 + x * -2) + x(-2 + x)) + 17 1 + 1x2 = ((4 + -2x) + x(-2 + x)) + 17 1 + 1x2 = (4 + -2x + (-2 * x + x * x)) + 17 1 + 1x2 = (4 + -2x + (-2x + x2)) + 17 Combine like terms: -2x + -2x = -4x 1 + 1x2 = (4 + -4x + x2) + 17 Reorder the terms: 1 + 1x2 = 4 + 17 + -4x + x2 Combine like terms: 4 + 17 = 21 1 + 1x2 = 21 + -4x + x2 Solving 1 + 1x2 = 21 + -4x + x2 Solving for variable 'x'. Reorder the terms: 1 + -21 + 4x + 1x2 + -1x2 = 21 + -4x + x2 + -21 + 4x + -1x2 Combine like terms: 1 + -21 = -20 -20 + 4x + 1x2 + -1x2 = 21 + -4x + x2 + -21 + 4x + -1x2 Combine like terms: 1x2 + -1x2 = 0 -20 + 4x + 0 = 21 + -4x + x2 + -21 + 4x + -1x2 -20 + 4x = 21 + -4x + x2 + -21 + 4x + -1x2 Reorder the terms: -20 + 4x = 21 + -21 + -4x + 4x + x2 + -1x2 Combine like terms: 21 + -21 = 0 -20 + 4x = 0 + -4x + 4x + x2 + -1x2 -20 + 4x = -4x + 4x + x2 + -1x2 Combine like terms: -4x + 4x = 0 -20 + 4x = 0 + x2 + -1x2 -20 + 4x = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -20 + 4x = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-5 + x) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Solution
x = {5}
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