Resolver (x-40)^2=p+1600

$$( x - 40 ) ^ { 2 } = p + 1600$$

Ebatzi: p

$$p=x\left(x-80\right)$$

Ebazpidea

\left(x-40\right)^{2} zabaltzeko, erabili Newton-en binomioa \left(a-b\right)^{2}=a^{2}-2ab+b^{2}.

$$x^{2}-80x+1600=p+1600$$

Trukatu aldeak, aldagaiak ezkerraldean egon daitezen.

$$p+1600=x^{2}-80x+1600$$

Kendu 1600 bi aldeetatik.

$$p=x^{2}-80x+1600-1600$$

0 lortzeko, 1600 balioari kendu 1600.

$$p=x^{2}-80x$$

Ebatzi: x (complex solution)

$$x=-\sqrt{p+1600}+40$$

$$x=\sqrt{p+1600}+40$$

Ebatzi: x

$$x=-\sqrt{p+1600}+40$$

$$x=\sqrt{p+1600}+40\text{, }p\geq -1600$$