Question
Solve equation by factorization : $(x – 4)^2 + 5^2 = 13^2$
✓
Answer
$(x – 4)^2 + 5^2 = 13^2$
$x^2 – 8x + 16 + 25 = 169$
$x^2- 8x + 41 - 169 = 0$
$\Rightarrow x^2- 8x - 128 = 0$
$\Rightarrow x^2 - 16x + 8x - 128 = 0$
$\Rightarrow x (x - 16) + 8(x - 16) = 0$
$\Rightarrow (x - 16) (x + 8) = 0$
Either $x - 16 = 0,$
then $x = 16$
or
$x + 8 = 0,$
then $x = -8$
Hence $x = 16, -8.$
$x^2 – 8x + 16 + 25 = 169$
$x^2- 8x + 41 - 169 = 0$
$\Rightarrow x^2- 8x - 128 = 0$
$\Rightarrow x^2 - 16x + 8x - 128 = 0$
$\Rightarrow x (x - 16) + 8(x - 16) = 0$
$\Rightarrow (x - 16) (x + 8) = 0$
Either $x - 16 = 0,$
then $x = 16$
or
$x + 8 = 0,$
then $x = -8$
Hence $x = 16, -8.$
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