Given system of equations are consistent
∴Δ=0
Δ=∣∣
∣
∣∣233c+2c+4c+6(c+2)2(c+4)2(c+6)2∣∣
∣
∣∣=0
C1→C1−C3;C2→C2−C3∣∣
∣
∣∣−103−4−2c+6−4(2c+8)−2(2c+10)(c+6)2∣∣
∣
∣∣=0⇒∣∣
∣
∣∣10341c+68c+322c+10(c+6)2∣∣
∣
∣∣=0C1→C1−4C2⇒∣∣
∣
∣∣10301c+6−82c+10(c+6)2∣∣
∣
∣∣=0C3→C3−3C1⇒∣∣
∣
∣∣10001c+6−82c+10(c+6)2+24∣∣
∣
∣∣=0⇒−c2−10c=0⇒c=0,c=−10
Sum of squares of values of c is 0+100=100