Solve Using the Square Root Property 36x^2-24x+4=9

$36 x^{2} - 24 x + 4 = 9$

Step 1

Subtract $9$ from both sides of the equation.

$36 x^{2} - 24 x + 4 - 9 = 0$

Step 2

Subtract $9$ from $4$ .

$36 x^{2} - 24 x - 5 = 0$

Step 3

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 36 \cdot - 5 = - 180$ and whose sum is $b = - 24$ .

Factor $- 24$ out of $- 24 x$ .

$36 x^{2} - 24 x - 5 = 0$

Rewrite $- 24$ as $6$ plus $- 30$

$36 x^{2} + (6 - 30) x - 5 = 0$

Apply the distributive property.

$36 x^{2} + 6 x - 30 x - 5 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(36 x^{2} + 6 x) - 30 x - 5 = 0$

Factor out the greatest common factor (GCF) from each group.

$6 x (6 x + 1) - 5 (6 x + 1) = 0$

Factor the polynomial by factoring out the greatest common factor, $6 x + 1$ .

$(6 x + 1) (6 x - 5) = 0$

Step 4

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

$6 x + 1 = 0$

$6 x - 5 = 0$

Step 5

Set $6 x + 1$ equal to $0$ and solve for $x$ .

Set $6 x + 1$ equal to $0$ .

$6 x + 1 = 0$

Solve $6 x + 1 = 0$ for $x$ .

Subtract $1$ from both sides of the equation.

$6 x = - 1$

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

Divide each term in $6 x = - 1$ by $6$ .

$\frac{6 x}{6} = \frac{- 1}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 1}{6}$

Divide $x$ by $1$ .

$x = \frac{- 1}{6}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{1}{6}$

Step 6

Set $6 x - 5$ equal to $0$ and solve for $x$ .

Set $6 x - 5$ equal to $0$ .

$6 x - 5 = 0$

Solve $6 x - 5 = 0$ for $x$ .

Add $5$ to both sides of the equation.

$6 x = 5$

Divide each term in $6 x = 5$ by $6$ and simplify.

Divide each term in $6 x = 5$ by $6$ .

$\frac{6 x}{6} = \frac{5}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 x}{6} = \frac{5}{6}$

Divide $x$ by $1$ .

$x = \frac{5}{6}$

Step 7

The final solution is all the values that make $(6 x + 1) (6 x - 5) = 0$ true.

$x = - \frac{1}{6}, \frac{5}{6}$

Solve Using the Square Root Property 36x^2-24x+4=9

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