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Simplifying (2x + 1)(2x + 3) = 10403 Reorder the terms: (1 + 2x)(2x + 3) = 10403 Reorder the terms: (1 + 2x)(3 + 2x) = 10403 Multiply (1 + 2x) * (3 + 2x) (1(3 + 2x) + 2x * (3 + 2x)) = 10403 ((3 * 1 + 2x * 1) + 2x * (3 + 2x)) = 10403 ((3 + 2x) + 2x * (3 + 2x)) = 10403 (3 + 2x + (3 * 2x + 2x * 2x)) = 10403 (3 + 2x + (6x + 4x2)) = 10403 Combine like terms: 2x + 6x = 8x (3 + 8x + 4x2) = 10403 Solving 3 + 8x + 4x2 = 10403 Solving for variable 'x'. Reorder the terms: 3 + -10403 + 8x + 4x2 = 10403 + -10403 Combine like terms: 3 + -10403 = -10400 -10400 + 8x + 4x2 = 10403 + -10403 Combine like terms: 10403 + -10403 = 0 -10400 + 8x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-2600 + 2x + x2) = 0 Factor a trinomial. 4((-52 + -1x)(50 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-52 + -1x)' equal to zero and attempt to solve: Simplifying -52 + -1x = 0 Solving -52 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '52' to each side of the equation. -52 + 52 + -1x = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -1x = 0 + 52 -1x = 0 + 52 Combine like terms: 0 + 52 = 52 -1x = 52 Divide each side by '-1'. x = -52 Simplifying x = -52Subproblem 2
Set the factor '(50 + -1x)' equal to zero and attempt to solve: Simplifying 50 + -1x = 0 Solving 50 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + -1x = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -1x = 0 + -50 -1x = 0 + -50 Combine like terms: 0 + -50 = -50 -1x = -50 Divide each side by '-1'. x = 50 Simplifying x = 50Solution
x = {-52, 50}
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