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Simplifying (4x + 1)(x + 1) = 175 Reorder the terms: (1 + 4x)(x + 1) = 175 Reorder the terms: (1 + 4x)(1 + x) = 175 Multiply (1 + 4x) * (1 + x) (1(1 + x) + 4x * (1 + x)) = 175 ((1 * 1 + x * 1) + 4x * (1 + x)) = 175 ((1 + 1x) + 4x * (1 + x)) = 175 (1 + 1x + (1 * 4x + x * 4x)) = 175 (1 + 1x + (4x + 4x2)) = 175 Combine like terms: 1x + 4x = 5x (1 + 5x + 4x2) = 175 Solving 1 + 5x + 4x2 = 175 Solving for variable 'x'. Reorder the terms: 1 + -175 + 5x + 4x2 = 175 + -175 Combine like terms: 1 + -175 = -174 -174 + 5x + 4x2 = 175 + -175 Combine like terms: 175 + -175 = 0 -174 + 5x + 4x2 = 0 Factor a trinomial. (-29 + -4x)(6 + -1x) = 0Subproblem 1
Set the factor '(-29 + -4x)' equal to zero and attempt to solve: Simplifying -29 + -4x = 0 Solving -29 + -4x = 0 Move all terms containing x to the left, all other terms to the right. Add '29' to each side of the equation. -29 + 29 + -4x = 0 + 29 Combine like terms: -29 + 29 = 0 0 + -4x = 0 + 29 -4x = 0 + 29 Combine like terms: 0 + 29 = 29 -4x = 29 Divide each side by '-4'. x = -7.25 Simplifying x = -7.25Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-7.25, 6}
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