Sure, let's solve the equation [tex]\( y = ax^2 + c \)[/tex] for [tex]\( x \)[/tex] step-by-step.
1. Start with the given equation:
[tex]\[ y = ax^2 + c \][/tex]
2. Isolate the term involving [tex]\( x \)[/tex]:
To do this, we need to move [tex]\( c \)[/tex] to the other side of the equation. Subtract [tex]\( c \)[/tex] from both sides:
[tex]\[ y - c = ax^2 \][/tex]
3. Solve for [tex]\( x^2 \)[/tex]:
To isolate [tex]\( x^2 \)[/tex], divide both sides by [tex]\( a \)[/tex]:
[tex]\[ \frac{y - c}{a} = x^2 \][/tex]
4. Solve for [tex]\( x \)[/tex]:
To solve for [tex]\( x \)[/tex], we need to take the square root of both sides. Remember that taking the square root introduces both positive and negative solutions:
[tex]\[ x = \pm \sqrt{\frac{y - c}{a}} \][/tex]
The correct solution for [tex]\( x \)[/tex] is:
[tex]\[ x = \pm \sqrt{\frac{y - c}{a}} \][/tex]
So, the correct answer from the given options is:
[tex]\[ x = \pm \sqrt{\frac{y - c}{a}} \][/tex]
