Fhaie041512viz
Answered

Write an equation using “x” and then solve the equation.
“In February, there were x museum pass holders admitted to
the museum. 68 of the visitors did not have a museum pass.

Sagot :

Princedennieldeguzmaviz

Answer:

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DanielLanoganviz

Write an equation using “x” and then solve the equation.

x= -3 and x=\frac{-3+/-3i\sqrt{3} }{2}

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

(x^3-a^3)=(x-a)(x^2+ax+a^2)

where a is the cube root of a^3.

here   this is 27 and the cube root of 27 is 3. so we write using the form:

(x-3)(x^2+(3)x+3^2)\\(x-3)(x^2+3x+9).

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

x=\frac{-b+/-\sqrt{b^2-4ac} }{2a}

where a = 1, b=3, and c=9

x=\frac{-3+/-\sqrt{3^2-4(1)(9)} }{2(1)} \\x=\frac{-3+/-\sqrt{9-36)} }{2} \\x=\frac{-3+/-\sqrt{-27)} }{2}\\x=\frac{-3+/-3i\sqrt{3} }{2}

this cubic has two complex roots.