Find the Perfect Square Trinomial 49x^2+bx+9

$49 x^{2} + b x + 9$

Step 1

Reorder $49 x^{2}$ and $b x$ .

$b x + 49 x^{2} + 9$

Step 2

Factor out the $49$

$49 (x^{2} + \frac{b x}{49} + \frac{9}{49})$

Step 3

To find the $c$ value $c = {(\frac{b}{2})}^{2}$ , divide the coefficient of $x$ by $2$ and square the result.

Multiply the numerator by the reciprocal of the denominator.

${(\frac{b}{49} \cdot \frac{1}{2})}^{2}$

Multiply $\frac{b}{49} \cdot \frac{1}{2}$ .

Multiply $\frac{b}{49}$ by $\frac{1}{2}$ .

${(\frac{b}{49 \cdot 2})}^{2}$

Multiply $49$ by $2$ .

${(\frac{b}{98})}^{2}$

Apply the product rule to $\frac{b}{98}$ .

$\frac{b^{2}}{98^{2}}$

Raise $98$ to the power of $2$ .

$\frac{b^{2}}{9604}$

Step 4

Add $\frac{b^{2}}{9604}$ to get the perfect square trinomial.

$49 (x^{2} + \frac{b x}{49} + \frac{9}{49} + \frac{b^{2}}{9604})$

Step 5

Simplify.

Apply the distributive property.

$49 x^{2} + 49 \frac{b x}{49} + 49 (\frac{9}{49}) + 49 \frac{b^{2}}{9604}$

Simplify.

Cancel the common factor of $49$ .

Cancel the common factor.

$49 x^{2} + 49 \frac{b x}{49} + 49 (\frac{9}{49}) + 49 \frac{b^{2}}{9604}$

Rewrite the expression.

$49 x^{2} + b x + 49 (\frac{9}{49}) + 49 \frac{b^{2}}{9604}$

Cancel the common factor of $49$ .

Cancel the common factor.

$49 x^{2} + b x + 49 (\frac{9}{49}) + 49 \frac{b^{2}}{9604}$

Rewrite the expression.

$49 x^{2} + b x + 9 + 49 \frac{b^{2}}{9604}$

Cancel the common factor of $49$ .

Factor $49$ out of $9604$ .

$49 x^{2} + b x + 9 + 49 \frac{b^{2}}{49 (196)}$

Cancel the common factor.

$49 x^{2} + b x + 9 + 49 \frac{b^{2}}{49 \cdot 196}$

Rewrite the expression.

$49 x^{2} + b x + 9 + \frac{b^{2}}{196}$