Solve q - 6 = the square root of 27 - 2q

Given the numerical statement:

q - 6 = Square root of 27 - 2q

Solution:

The given numerical statement can be written as, 

q - 6 = √(27 - 2q)

In order to solve the given equation, we start first by squaring both sides of the equation to cancel out the square root sign.

q - 6 = √(27 - 2q)

(q - 6 )^2= (√(27 - 2q))^2

q^2 - 12q + 36 = 27 - 2q

Transpose 27 and -2q on the other side of the equation, hence we must take note that in transposing a number, the sign changes.

= q^2 - 12q + 36 - 27 - 2q 

= q^2 - 14q + 9

a = 1

b = -14

c = 9

Now if we want to find for the value of q, we can apply the quadratic formula.

The Quadratic formula:

x = −b ± √(b^2 − 4ac)/2a

is used to solve quadratic equations where a ≠ 0, in the form
ax^2+bx+c=0

When b^2−4ac=0 there is one real root.

When b^2−4ac>0 there are two real roots.

When b^2−4ac<0 there are no real roots, only a complex number.

Substitute the given values of a, b and c to the quadratic formula.

x = −b ± √(b^2 − 4ac)/2a
x = −(-14) ± √((-14)^2 − 4(1)(9))/2(1)
x = 14 ± √( 144 - 36)/2
x = 14 ± √(108)/2
x = 14 ± 10.39/2

Solve for + - separately

x = 14 + 10.39/2
x = 24.39/2
x = 12 .2

x = 14 - 10.39/2
x = 4.39/2
x = 2.2

Final answer:

x = 12.2

x = 2.2