Question

Solve by completing a square r^2-8r+9

Answer 1

Solving  $r^2-8r+9$ by completing a square gives $(r+4)^2-7$

Step-by-step explanation:

We need to solve the equation $r^2-8r+9$ by completing a square

The completing a square method requires: $a^2\pm 2ab +b^2=(a\pm b)^2$

Solving:

$r^2-8r+9\\=(r)^2-2(r)(?)+(?)^2+9$

We need to add and subtract (4)^2=16 to make the equation a complete square

$=(r)^2-2(r)(4)+(4)^2-(4)^2+9\\=(r)^2-2(r)(4)+(4)^2-16+9\\=(r)^2-2(r)(4)+(4)^2-7\\=(r+4)^2-7$

So, Solving  $r^2-8r+9$ by completing a square gives $(r+4)^2-7$

Keywords: Solve by completing a square

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