Question
Solve the following equations for the unknown: $(6p + 9)^2 + (8p - 7)^2 = (10p + 3)^2 - 71$
✓
Answer
$(6p + 9)^2 + (8p - 7)^2 = (10p + 3)^2 - 71$
$[36p^2 + 81 + 2(6p)(9)] + [64p^2 + 49 - 2(8p)(7)] = 100p^2 + 9 + 2(10p)(3) - 71$
$\Rightarrow 100p^2 + 130 + 2 \times 54p - 2 \times 54p - 2 \times 56p$
$= 100p^2 + 9 - 71 + 60p$
Collecting like terms,
$\Rightarrow 130 + 71 - 9 = 60p + 4p$
$\Rightarrow 192 = 64p$
$\Rightarrow p = 3.$
$[36p^2 + 81 + 2(6p)(9)] + [64p^2 + 49 - 2(8p)(7)] = 100p^2 + 9 + 2(10p)(3) - 71$
$\Rightarrow 100p^2 + 130 + 2 \times 54p - 2 \times 54p - 2 \times 56p$
$= 100p^2 + 9 - 71 + 60p$
Collecting like terms,
$\Rightarrow 130 + 71 - 9 = 60p + 4p$
$\Rightarrow 192 = 64p$
$\Rightarrow p = 3.$
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