How do you solve -3( x - 2) ^ { 2} - 33= 0?

2 Answers
Sep 27, 2017

Solution : x ~~ 2 + 3.32 i , x ~~ 2 - 3.32 i

Explanation:

-3 (x-2)^2 -33=0 or 3(x-2)^2= -33 or

(x-2)^2= -11 or (x-2)= +-sqrt (-11) or

(x-2)=+-sqrt (11i^2)or x = 2 +- sqrt11 i

[i^2=-1] :. x = 2+sqrt 11 i , x = 2- sqrt 11 i or

x ~~ 2 + 3.32 i (2dp) , x ~~ 2 - 3.32 i (2dp)

Solution : x ~~ 2 + 3.32 i , x ~~ 2 - 3.32 i [Ans]

Sep 27, 2017

See below.

Explanation:

-3(x-2)^2-33=0

Add 33 to both sides:

-3(x-2)^2=33

Divide both sides by -3:

(x-2)^2=-11

Take square roots of both sides:

x-2 = sqrt(-11

x = 2+-sqrt(-11)

Notice sqrt(-11) => sqrt(11xx-1)=>sqrt(11)sqrt(-1)

sqrt(-1) =color(red)( i) => sqrt(11)color(red)(i)

color(red)(i) is known as the imaginary unit.

This is sometimes written isqrt(11) to avoid any confusion.

So now we have:

x= 2+-sqrt(11)color(red)(i)=> x= 2+-color(red)(i)sqrt(11)

x=2+color(red)(i)sqrt(11) , x= 2 - color(red)(i)sqrt(11)

These are referred to as imaginary roots. These occur because the parabola neither crosses nor turns at the x axis, which indicates that no real number can satisfy the equation -3(x-2)^2-33=0

Graph: graph{y=-3(x-2)^2-33 [-30, 30, -400, 50]}