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Simplifying 22675 = x2 + 30x + 400 Reorder the terms: 22675 = 400 + 30x + x2 Solving 22675 = 400 + 30x + x2 Solving for variable 'x'. Combine like terms: 22675 + -400 = 22275 22275 + -30x + -1x2 = 400 + 30x + x2 + -400 + -30x + -1x2 Reorder the terms: 22275 + -30x + -1x2 = 400 + -400 + 30x + -30x + x2 + -1x2 Combine like terms: 400 + -400 = 0 22275 + -30x + -1x2 = 0 + 30x + -30x + x2 + -1x2 22275 + -30x + -1x2 = 30x + -30x + x2 + -1x2 Combine like terms: 30x + -30x = 0 22275 + -30x + -1x2 = 0 + x2 + -1x2 22275 + -30x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 22275 + -30x + -1x2 = 0 Factor a trinomial. (135 + -1x)(165 + x) = 0Subproblem 1
Set the factor '(135 + -1x)' equal to zero and attempt to solve: Simplifying 135 + -1x = 0 Solving 135 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-135' to each side of the equation. 135 + -135 + -1x = 0 + -135 Combine like terms: 135 + -135 = 0 0 + -1x = 0 + -135 -1x = 0 + -135 Combine like terms: 0 + -135 = -135 -1x = -135 Divide each side by '-1'. x = 135 Simplifying x = 135Subproblem 2
Set the factor '(165 + x)' equal to zero and attempt to solve: Simplifying 165 + x = 0 Solving 165 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-165' to each side of the equation. 165 + -165 + x = 0 + -165 Combine like terms: 165 + -165 = 0 0 + x = 0 + -165 x = 0 + -165 Combine like terms: 0 + -165 = -165 x = -165 Simplifying x = -165Solution
x = {135, -165}
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