(5x-4)(5x-4)=121

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Solution for (5x-4)(5x-4)=121 equation:


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 = -1.4

Subproblem 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 = 3

Solution

x = {-1.4, 3}

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