## Algebra 1: Common Core (15th Edition)

Width of walkway,$x=3.1$ ft
Area of the walkway=$(2x+42)(2x+26)-26 \times 42$ Thus, $4x^2+136x=460$ Re-write the equations as: $x^2+34x=115$ Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=34$ To complete the square, add $\dfrac{(34)^2}{4}=289$ on both sides. $x^2+34x+289=115+289$ $\implies (x+17)^2=404$ Neglecting the negative sign, we have $\implies (x+17)=20.1$ $x=3.1$ ft Width of walkway,$x=3.1$ ft