Solve Using the Square Root Property 4x^2+4x+1=16

$4 x^{2} + 4 x + 1 = 16$

Step 1

Subtract $16$ from both sides of the equation.

$4 x^{2} + 4 x + 1 - 16 = 0$

Step 2

Subtract $16$ from $1$ .

$4 x^{2} + 4 x - 15 = 0$

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 $a \cdot c = 4 \cdot - 15 = - 60$ and whose sum is $b = 4$ .

Factor $4$ out of $4 x$ .

$4 x^{2} + 4 (x) - 15 = 0$

Rewrite $4$ as $- 6$ plus $10$

$4 x^{2} + (- 6 + 10) x - 15 = 0$

Apply the distributive property.

$4 x^{2} - 6 x + 10 x - 15 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(4 x^{2} - 6 x) + 10 x - 15 = 0$

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

$2 x (2 x - 3) + 5 (2 x - 3) = 0$

Factor the polynomial by factoring out the greatest common factor, $2 x - 3$ .

$(2 x - 3) (2 x + 5) = 0$

Step 4

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

$2 x - 3 = 0$

$2 x + 5 = 0$

Step 5

Set $2 x - 3$ equal to $0$ and solve for $x$ .

Set $2 x - 3$ equal to $0$ .

$2 x - 3 = 0$

Solve $2 x - 3 = 0$ for $x$ .

Add $3$ to both sides of the equation.

$2 x = 3$

Divide each term in $2 x = 3$ by $2$ and simplify.

Divide each term in $2 x = 3$ by $2$ .

$\frac{2 x}{2} = \frac{3}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{3}{2}$

Divide $x$ by $1$ .

$x = \frac{3}{2}$

Step 6

Set $2 x + 5$ equal to $0$ and solve for $x$ .

Set $2 x + 5$ equal to $0$ .

$2 x + 5 = 0$

Solve $2 x + 5 = 0$ for $x$ .

Subtract $5$ from both sides of the equation.

$2 x = - 5$

Divide each term in $2 x = - 5$ by $2$ and simplify.

Divide each term in $2 x = - 5$ by $2$ .

$\frac{2 x}{2} = \frac{- 5}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 5}{2}$

Divide $x$ by $1$ .

$x = \frac{- 5}{2}$

Simplify the right side.

Move the negative in front of the fraction.

$x = - \frac{5}{2}$

Step 7

The final solution is all the values that make $(2 x - 3) (2 x + 5) = 0$ true.

$x = \frac{3}{2}, - \frac{5}{2}$

Solve Using the Square Root Property 4x^2+4x+1=16

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