Solve Using the Square Root Property 36=(t^2-t)/2

$36 = \frac{t^{2} - t}{2}$

Step 1

Rewrite the equation as $\frac{t^{2} - t}{2} = 36$ .

$\frac{t^{2} - t}{2} = 36$

Step 2

Multiply both sides of the equation by $2$ .

$2 \frac{t^{2} - t}{2} = 2 \cdot 36$

Step 3

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{t^{2} - t}{2} = 2 \cdot 36$

Rewrite the expression.

$t^{2} - t = 2 \cdot 36$

Simplify the right side.

Multiply $2$ by $36$ .

$t^{2} - t = 72$

Step 4

Subtract $72$ from both sides of the equation.

$t^{2} - t - 72 = 0$

Step 5

Factor $t^{2} - t - 72$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 72$ and whose sum is $- 1$ .

$- 9, 8$

Write the factored form using these integers.

$(t - 9) (t + 8) = 0$

Step 6

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$t - 9 = 0$

$t + 8 = 0$

Step 7

Set $t - 9$ equal to $0$ and solve for $t$ .

Set $t - 9$ equal to $0$ .

$t - 9 = 0$

Add $9$ to both sides of the equation.

$t = 9$

Step 8

Set $t + 8$ equal to $0$ and solve for $t$ .

Set $t + 8$ equal to $0$ .

$t + 8 = 0$

Subtract $8$ from both sides of the equation.

$t = - 8$

Step 9

The final solution is all the values that make $(t - 9) (t + 8) = 0$ true.

$t = 9, - 8$

Solve Using the Square Root Property 36=(t^2-t)/2

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