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Simplifying 4x2 + -12x + 9 = 289 Reorder the terms: 9 + -12x + 4x2 = 289 Solving 9 + -12x + 4x2 = 289 Solving for variable 'x'. Reorder the terms: 9 + -289 + -12x + 4x2 = 289 + -289 Combine like terms: 9 + -289 = -280 -280 + -12x + 4x2 = 289 + -289 Combine like terms: 289 + -289 = 0 -280 + -12x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-70 + -3x + x2) = 0 Factor a trinomial. 4((-7 + -1x)(10 + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {-7, 10}
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