Variable

Find variable P:

PP plus P x P plus P = 160

Result

P =  8

Solution:

10 P+P+P P+P=160 10P+P+PP+P=160  10 P+P+P P+P=160 P2+12P160=0  a=1;b=12;c=160 D=b24ac=12241(160)=784 D>0  P1,2=b±D2a=12±7842 P1,2=12±282 P1,2=6±14 P1=8 P2=20   Factored form of the equation:  (P8)(P+20)=0 P>0 P=P1=8 s=88+8 8+8=16010 \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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