Precalculus Examples

$36 t^{2} - 12 t + 1 = 0$

Step 1

Factor using the perfect square rule.

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Step 1.1

Rewrite $36 t^{2}$ as ${(6 t)}^{2}$ .

${(6 t)}^{2} - 12 t + 1 = 0$

Step 1.2

Rewrite $1$ as $1^{2}$ .

${(6 t)}^{2} - 12 t + 1^{2} = 0$

Step 1.3

Check that the middle term is two times the product of the numbers being squared in the first term and third term.

$12 t = 2 \cdot (6 t) \cdot 1$

Step 1.4

Rewrite the polynomial.

${(6 t)}^{2} - 2 \cdot (6 t) \cdot 1 + 1^{2} = 0$

Step 1.5

Factor using the perfect square trinomial rule $a^{2} - 2 a b + b^{2} = {(a - b)}^{2}$ , where $a = 6 t$ and $b = 1$ .

${(6 t - 1)}^{2} = 0$

Step 2

Set the $6 t - 1$ equal to $0$ .

$6 t - 1 = 0$

Step 3

Solve for $t$ .

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Step 3.1

Add $1$ to both sides of the equation.

$6 t = 1$

Step 3.2

Divide each term in $6 t = 1$ by $6$ and simplify.

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Step 3.2.1

Divide each term in $6 t = 1$ by $6$ .

$\frac{6 t}{6} = \frac{1}{6}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $6$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{6 t}{6} = \frac{1}{6}$

Step 3.2.2.1.2

Divide $t$ by $1$ .

$t = \frac{1}{6}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$t = \frac{1}{6}$

Decimal Form:

$t = 0.1\overline{6}$