Divide both sides of the equation by 9:
x^2 + 64/3x + 256/9 = 0x2+643x+2569=0
Add a^2 - 256/9a2−2569 to both sides of the equation:
x^2 + 64/3x + a^2 = a^2 - 256/9x2+643x+a2=a2−2569
Set the middle term in the right side of the pattern, (x + a)^2 = x^2 + 2ax + a^2(x+a)2=x2+2ax+a2 equal to the middle term in the equation:
2ax = 64/3x2ax=643x
Solve for a:
a = 32/3a=323
Substitute the left side of the pattern into the left side of the equation:
(x + a)^2 = a^2 - 256/9(x+a)2=a2−2569
Substitute 32/3323 for every "a":
(x + 32/3)^2 = (32/3)^2 - 256/9(x+323)2=(323)2−2569
Simplify the right side:
(x + 32/3)^2 = 256/3(x+323)2=2563
Use the square root on both sides:
x + 32/3 = +-(16sqrt(3))/3x+323=±16√33
Subtract 32/3323 from both sides:
x = (-32 +-16sqrt(3))/3x=−32±16√33
x = (-32 + 16sqrt(3))/3 and x = (-32 -16sqrt(3))/3x=−32+16√33andx=−32−16√33
