Factor the expression -x^2+14x+57

 Exercise

$-x^2+14x+57$

 

Use the complete the square method to factor the trinomial of the form $ax^2+bx+c$. Take common factor $a$ ($-1$) to all terms

$-\left(x^2-14x-57\right)$

 

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

$-\left(x^2-14x-57+49-49\right)$

 

Factor the perfect square trinomial $x^2+-14x+49$

$-\left(\left(x-7\right)^2-57-49\right)$

 

Subtract the values $-57$ and $-49$

$-\left(\left(x-7\right)^2-106\right)$

 

Solve the product $-\left(\left(x-7\right)^2-106\right)$

$-\left(x-7\right)^2+106$

$-\left(x-7\right)^2+106$

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