Question
An equation is shown.
y=-5h^2+gh-16
What is the equation, solved for
?
y=-5h^2+gh-16
What is the equation, solved for
?
Answers
GPT-4o mini
It looks like you're asking to solve the equation \( y = -5h^2 + gh - 16 \) for one of the variables, but you didn't specify which variable you want to solve for.
I'll show you how to solve for both \( h \) and \( g \).
1. **Solving for \( h \)**:
To solve for \( h \), you can rewrite the equation in the form of a standard quadratic equation:
\[
-5h^2 + gh - (y + 16) = 0
\]
This is a quadratic equation in \( h \). To apply the quadratic formula \( h = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = -5 \), \( b = g \), and \( c = -(y + 16) \):
\[
h = \frac{-g \pm \sqrt{g^2 - 4 \cdot (-5) \cdot (-(y + 16))}}{2 \cdot (-5)}
\]
This simplifies to:
\[
h = \frac{-g \pm \sqrt{g^2 + 20(y + 16)}}{-10}
\]
2. **Solving for \( g \)**:
To solve for \( g \), you can rearrange the original equation as follows:
\[
gh = 5h^2 + y + 16
\]
Now, divide both sides by \( h \) (assuming \( h \neq 0 \)):
\[
g = \frac{5h^2 + y + 16}{h}
\]
If you specify the variable you want to solve for, I can provide a more focused solution.
I'll show you how to solve for both \( h \) and \( g \).
1. **Solving for \( h \)**:
To solve for \( h \), you can rewrite the equation in the form of a standard quadratic equation:
\[
-5h^2 + gh - (y + 16) = 0
\]
This is a quadratic equation in \( h \). To apply the quadratic formula \( h = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = -5 \), \( b = g \), and \( c = -(y + 16) \):
\[
h = \frac{-g \pm \sqrt{g^2 - 4 \cdot (-5) \cdot (-(y + 16))}}{2 \cdot (-5)}
\]
This simplifies to:
\[
h = \frac{-g \pm \sqrt{g^2 + 20(y + 16)}}{-10}
\]
2. **Solving for \( g \)**:
To solve for \( g \), you can rearrange the original equation as follows:
\[
gh = 5h^2 + y + 16
\]
Now, divide both sides by \( h \) (assuming \( h \neq 0 \)):
\[
g = \frac{5h^2 + y + 16}{h}
\]
If you specify the variable you want to solve for, I can provide a more focused solution.