Alright, let's solve the given equation step-by-step:
The given equation is:
[tex]\[ -4 = a(0 + 4)^2 - 12 \][/tex]
First, simplify the expression inside the parentheses:
[tex]\[ 0 + 4 = 4 \][/tex]
So the equation becomes:
[tex]\[ -4 = a(4)^2 - 12 \][/tex]
Next, calculate the square of 4:
[tex]\[ 4^2 = 16 \][/tex]
Substitute this back into the equation:
[tex]\[ -4 = a \cdot 16 - 12 \][/tex]
Now, isolate the term involving [tex]\( a \)[/tex]. To do this, add 12 to both sides of the equation:
[tex]\[ -4 + 12 = a \cdot 16 - 12 + 12 \][/tex]
This simplifies to:
[tex]\[ 8 = a \cdot 16 \][/tex]
To solve for [tex]\( a \)[/tex], divide both sides by 16:
[tex]\[ a = \frac{8}{16} \][/tex]
Simplify the fraction:
[tex]\[ a = 0.5 \][/tex]
Therefore, the value of [tex]\( a \)[/tex] is:
[tex]\[ a = 0.5 \][/tex]
