Question

solve the equation by completing the square and applying the square root property. write answers in exact, simplified form.
$t^{2}=2t + 5$
the solution set is {}

Explanation:

Step1: Rearrange the equation

$t^{2}-2t - 5=0$

Step2: Complete the square

The coefficient of $t$ is $- 2$. Half of it is $-1$, and its square is $1$.
Add and subtract $1$ on the left - hand side of the equation:
$t^{2}-2t + 1-1 - 5=0$, which can be rewritten as $(t - 1)^{2}-6=0$.
Then $(t - 1)^{2}=6$.

Step3: Apply the square - root property

$t-1=\pm\sqrt{6}$.

Step4: Solve for $t$

$t = 1\pm\sqrt{6}$.

Answer:

$\{1+\sqrt{6},1 - \sqrt{6}\}$