Solve the equation by factoring, by finding square roots, or by using the quadratic formula.
3(x+4)^2= -27
3 ( x + 4 ) ^ 2 = - 27 Divide both sides with 3
( x + 4 ) ^ 2 = - 9
The left hand side is a perfect square,so you can apply the square root method :
x + 4 = + OR - sqrt ( - 9 )
x = + OR - sqrt ( - 9 )- 4
( Remark:
sqrt ( - 9 ) = sqrt ( - 1 * 3 ^ 2 ) =
+ OR - 3i
where i = Imaginary unit = sqrt ( - 1 )
)
x = + OR - ( 3 i ) - 4
post it.
To solve the given equation 3(x+4)^2 = -27, we'll start by dividing both sides of the equation by 3:
(x+4)^2 = -27/3
Simplifying further, we have:
(x+4)^2 = -9
To solve this equation, we could use either factoring, finding square roots, or the quadratic formula. Let's use the method of finding square roots:
Taking the square root of both sides of the equation, we get:
√[(x+4)^2] = ±√(-9)
Simplifying further, we have:
x+4 = ±√(-9)
Since we have a negative number inside the square root, the equation has no real solutions. The square root of a negative number is imaginary.
Hence, the equation 3(x+4)^2 = -27 has no solution in the set of real numbers.