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Simplifying 4x2 + -168x + 1764 = 400 Reorder the terms: 1764 + -168x + 4x2 = 400 Solving 1764 + -168x + 4x2 = 400 Solving for variable 'x'. Reorder the terms: 1764 + -400 + -168x + 4x2 = 400 + -400 Combine like terms: 1764 + -400 = 1364 1364 + -168x + 4x2 = 400 + -400 Combine like terms: 400 + -400 = 0 1364 + -168x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(341 + -42x + x2) = 0 Factor a trinomial. 4((11 + -1x)(31 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(11 + -1x)' equal to zero and attempt to solve: Simplifying 11 + -1x = 0 Solving 11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1x = 0 + -11 -1x = 0 + -11 Combine like terms: 0 + -11 = -11 -1x = -11 Divide each side by '-1'. x = 11 Simplifying x = 11Subproblem 2
Set the factor '(31 + -1x)' equal to zero and attempt to solve: Simplifying 31 + -1x = 0 Solving 31 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-31' to each side of the equation. 31 + -31 + -1x = 0 + -31 Combine like terms: 31 + -31 = 0 0 + -1x = 0 + -31 -1x = 0 + -31 Combine like terms: 0 + -31 = -31 -1x = -31 Divide each side by '-1'. x = 31 Simplifying x = 31Solution
x = {11, 31}
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