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Simplifying (5x + -4)(5x + -4) = 121 Reorder the terms: (-4 + 5x)(5x + -4) = 121 Reorder the terms: (-4 + 5x)(-4 + 5x) = 121 Multiply (-4 + 5x) * (-4 + 5x) (-4(-4 + 5x) + 5x * (-4 + 5x)) = 121 ((-4 * -4 + 5x * -4) + 5x * (-4 + 5x)) = 121 ((16 + -20x) + 5x * (-4 + 5x)) = 121 (16 + -20x + (-4 * 5x + 5x * 5x)) = 121 (16 + -20x + (-20x + 25x2)) = 121 Combine like terms: -20x + -20x = -40x (16 + -40x + 25x2) = 121 Solving 16 + -40x + 25x2 = 121 Solving for variable 'x'. Reorder the terms: 16 + -121 + -40x + 25x2 = 121 + -121 Combine like terms: 16 + -121 = -105 -105 + -40x + 25x2 = 121 + -121 Combine like terms: 121 + -121 = 0 -105 + -40x + 25x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-21 + -8x + 5x2) = 0 Factor a trinomial. 5((-7 + -5x)(3 + -1x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-7 + -5x)' equal to zero and attempt to solve: Simplifying -7 + -5x = 0 Solving -7 + -5x = 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 + -5x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -5x = 0 + 7 -5x = 0 + 7 Combine like terms: 0 + 7 = 7 -5x = 7 Divide each side by '-5'. x = -1.4 Simplifying x = -1.4Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-1.4, 3}
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