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Simplifying
(3x + 5)(3x + 5) = 169 + 30x
Reorder the terms:
(5 + 3x)(3x + 5) = 169 + 30x
Reorder the terms:
(5 + 3x)(5 + 3x) = 169 + 30x
Multiply (5 + 3x) * (5 + 3x)
(5(5 + 3x) + 3x * (5 + 3x)) = 169 + 30x
((5 * 5 + 3x * 5) + 3x * (5 + 3x)) = 169 + 30x
((25 + 15x) + 3x * (5 + 3x)) = 169 + 30x
(25 + 15x + (5 * 3x + 3x * 3x)) = 169 + 30x
(25 + 15x + (15x + 9x2)) = 169 + 30x
Combine like terms: 15x + 15x = 30x
(25 + 30x + 9x2) = 169 + 30x
Add '-30x' to each side of the equation.
25 + 30x + -30x + 9x2 = 169 + 30x + -30x
Combine like terms: 30x + -30x = 0
25 + 0 + 9x2 = 169 + 30x + -30x
25 + 9x2 = 169 + 30x + -30x
Combine like terms: 30x + -30x = 0
25 + 9x2 = 169 + 0
25 + 9x2 = 169
Solving
25 + 9x2 = 169
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-25' to each side of the equation.
25 + -25 + 9x2 = 169 + -25
Combine like terms: 25 + -25 = 0
0 + 9x2 = 169 + -25
9x2 = 169 + -25
Combine like terms: 169 + -25 = 144
9x2 = 144
Divide each side by '9'.
x2 = 16
Simplifying
x2 = 16
Take the square root of each side:
x = {-4, 4}
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