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Simplifying
75 = (2x + 5)(2x + -5)
Reorder the terms:
75 = (5 + 2x)(2x + -5)
Reorder the terms:
75 = (5 + 2x)(-5 + 2x)
Multiply (5 + 2x) * (-5 + 2x)
75 = (5(-5 + 2x) + 2x * (-5 + 2x))
75 = ((-5 * 5 + 2x * 5) + 2x * (-5 + 2x))
75 = ((-25 + 10x) + 2x * (-5 + 2x))
75 = (-25 + 10x + (-5 * 2x + 2x * 2x))
75 = (-25 + 10x + (-10x + 4x2))
Combine like terms: 10x + -10x = 0
75 = (-25 + 0 + 4x2)
75 = (-25 + 4x2)
Solving
75 = -25 + 4x2
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-4x2' to each side of the equation.
75 + -4x2 = -25 + 4x2 + -4x2
Combine like terms: 4x2 + -4x2 = 0
75 + -4x2 = -25 + 0
75 + -4x2 = -25
Add '-75' to each side of the equation.
75 + -75 + -4x2 = -25 + -75
Combine like terms: 75 + -75 = 0
0 + -4x2 = -25 + -75
-4x2 = -25 + -75
Combine like terms: -25 + -75 = -100
-4x2 = -100
Divide each side by '-4'.
x2 = 25
Simplifying
x2 = 25
Take the square root of each side:
x = {-5, 5}
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