Certainly! Let's solve the equation [tex]\( d^2 - 12d + 36 = 4 \)[/tex] step-by-step using the square roots property.
1. First, bring the equation to standard form:
[tex]\[
d^2 - 12d + 36 - 4 = 0
\][/tex]
Which simplifies to:
[tex]\[
d^2 - 12d + 32 = 0
\][/tex]
2. Next, notice that the equation is a perfect square trinomial:
[tex]\[
(d - 6)^2 = 4
\][/tex]
3. Apply the square root property:
[tex]\[
d - 6 = \pm 2
\][/tex]
This gives us two equations to solve:
[tex]\[
\begin{cases}
d - 6 = 2 \\
d - 6 = -2
\end{cases}
\][/tex]
4. Solve each equation individually:
[tex]\[
\begin{cases}
d - 6 = 2 & \Rightarrow d = 2 + 6 = 8 \\
d - 6 = -2 & \Rightarrow d = -2 + 6 = 4
\end{cases}
\][/tex]
So, the solutions to the equation [tex]\( d^2 - 12d + 36 = 4 \)[/tex] are:
[tex]\[
d = 8, 4
\][/tex]
