# Variable

Find variable P:

PP plus P x P plus P = 160

Result

P =  8

#### Solution:

$10 \cdot \ P+P+P \cdot \ P+P=160 \ \\ 10*P+P+P*P+P=160 \ \\ \ \\ 10 \cdot \ P+P+P \cdot \ P+P=160 \ \\ P^2 +12P -160=0 \ \\ \ \\ a=1; b=12; c=-160 \ \\ D=b^2 - 4ac=12^2 - 4\cdot 1 \cdot (-160)=784 \ \\ D>0 \ \\ \ \\ P_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ -12 \pm \sqrt{ 784 } }{ 2 } \ \\ P_{1,2}=\dfrac{ -12 \pm 28 }{ 2 } \ \\ P_{1,2}=-6 \pm 14 \ \\ P_{1}=8 \ \\ P_{2}=-20 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ (P -8) (P +20)=0 \ \\ P>0 \ \\ P=P_{1}=8 \ \\ s=88+8 \cdot \ 8+8=160$

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