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Simplifying 175 = 4x2 + 5x + 1 Reorder the terms: 175 = 1 + 5x + 4x2 Solving 175 = 1 + 5x + 4x2 Solving for variable 'x'. Combine like terms: 175 + -1 = 174 174 + -5x + -4x2 = 1 + 5x + 4x2 + -1 + -5x + -4x2 Reorder the terms: 174 + -5x + -4x2 = 1 + -1 + 5x + -5x + 4x2 + -4x2 Combine like terms: 1 + -1 = 0 174 + -5x + -4x2 = 0 + 5x + -5x + 4x2 + -4x2 174 + -5x + -4x2 = 5x + -5x + 4x2 + -4x2 Combine like terms: 5x + -5x = 0 174 + -5x + -4x2 = 0 + 4x2 + -4x2 174 + -5x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 174 + -5x + -4x2 = 0 Factor a trinomial. (6 + -1x)(29 + 4x) = 0Subproblem 1
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 = 6Subproblem 2
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 = -7.25Solution
x = {6, -7.25}
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