Factor the expression 30x^2+7x+15

 Exercise

$30x^2+7x+15$

 

Use the complete the square method to factor the trinomial of the form $ax^2+bx+c$. Take common factor $a$ ($30$) to all terms

$30\left(x^2+\frac{7}{30}x+\frac{1}{2}\right)$

 

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

$30\left(x^2+\frac{7}{30}x+\frac{1}{2}+\frac{49}{3600}-\frac{49}{3600}\right)$

 

Factor the perfect square trinomial $x^2+\frac{7}{30}x+\frac{49}{3600}$

$30\left(\left(x+\frac{7}{60}\right)^2+\frac{1}{2}-\frac{49}{3600}\right)$

 

Solve the product $30\left(\left(x+\frac{7}{60}\right)^2+\frac{1}{2}-\frac{49}{3600}\right)$

$30\left(x+\frac{7}{60}\right)^2+30\cdot \left(\frac{1}{2}-\frac{49}{3600}\right)$

$30\left(x+\frac{7}{60}\right)^2+30\cdot \left(\frac{1}{2}-\frac{49}{3600}\right)$

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