x * (4x + 7) =480, solve for x
Solve for x:
x (4 x + 7) = 480
Expand out terms of the left hand side:
4 x^2 + 7 x = 480
Divide both sides by 4:
x^2 + (7 x)/4 = 120
Add 49/64 to both sides:
x^2 + (7 x)/4 + 49/64 = 7729/64
Write the left hand side as a square:
(x + 7/8)^2 = 7729/64
Take the square root of both sides:
x + 7/8 = sqrt(7729)/8 or x + 7/8 = -sqrt(7729)/8
Subtract 7/8 from both sides:
x = sqrt(7729)/8 - 7/8 or x + 7/8 = -sqrt(7729)/8
Subtract 7/8 from both sides:
Answer: | x = sqrt(7729)/8 - 7/8 =~10.11 inches.
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