Factor the expression 9x^2-14x+-15

 Exercise

$9x^2-14x-15$

 

Use the complete the square method to factor the trinomial of the form $ax^2+bx+c$. Take common factor $a$ ($9$) to all terms

$9\left(x^2-\frac{14}{9}x-\frac{5}{3}\right)$

 

Add and subtract $\displaystyle\left(\frac{b}{2a}\right)^2$

$9\left(x^2-\frac{14}{9}x-\frac{5}{3}+\frac{49}{81}-\frac{49}{81}\right)$

 

Factor the perfect square trinomial $x^2+-\frac{14}{9}x+\frac{49}{81}$

$9\left(\left(x- \frac{7}{9}\right)^2-\frac{5}{3}-\frac{49}{81}\right)$

 

Multiply the fraction and term in $- \frac{7}{9}$

$9\left(\left(x-\frac{7}{9}\right)^2-\frac{5}{3}-\frac{49}{81}\right)$

 

Solve the product $9\left(\left(x-\frac{7}{9}\right)^2-\frac{5}{3}-\frac{49}{81}\right)$

$9\left(x-\frac{7}{9}\right)^2+9\cdot \left(-\frac{5}{3}-\frac{49}{81}\right)$

$9\left(x-\frac{7}{9}\right)^2+9\cdot \left(-\frac{5}{3}-\frac{49}{81}\right)$

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