To solve the given equation [tex]\( c^2 = a^2 + b^2 - 2ab d \)[/tex] for [tex]\( d \)[/tex], follow these steps:
1. Start with the given equation:
[tex]\[ c^2 = a^2 + b^2 - 2ab d \][/tex]
2. Isolate the term involving [tex]\( d \)[/tex] on one side of the equation.
First, subtract [tex]\( a^2 \)[/tex] and [tex]\( b^2 \)[/tex] from both sides:
[tex]\[ c^2 - a^2 - b^2 = -2ab d \][/tex]
3. Next, solve for [tex]\( d \)[/tex] by isolating it:
Divide both sides by [tex]\(-2ab\)[/tex]:
[tex]\[ d = \frac{c^2 - a^2 - b^2}{-2ab} \][/tex]
4. Simplify the equation:
Notice that dividing by a negative sign will change the sign of each term in the numerator:
[tex]\[ d = \frac{-(a^2 + b^2 - c^2)}{2ab} \][/tex]
Simplifying further, we get:
[tex]\[ d = \frac{a^2 + b^2 - c^2}{2ab} \][/tex]
Thus, the solution for [tex]\( d \)[/tex] is:
[tex]\[ d = \frac{a^2 + b^2 - c^2}{2ab} \][/tex]
