Answer
$x=13.3$ in
Work Step by Step
Area of a rectangle = Length x Breadth
Thus, $(2+x)x=420$
Re-write the equations as: $2x^2+5x=420$
or, $x^2+\frac{5}{2}x=210$
Compare it with the standard form of quadratic equation $ax^2+bx+c$, we have $a=1, b=\frac{5}{2}$
Therefore, $b^2=4ac$ $\implies$ $c=\dfrac{b^2}{4a}$
Thus, $c=\dfrac{b^2}{4a}=\dfrac{(\frac{5}{2})^2}{4}=\dfrac{25}{16}$
To complete the square, add $\dfrac{25}{16}$ on both sides.
$x^2+\frac{5}{2}x+\dfrac{25}{16}=210+\dfrac{25}{16}$
$\implies (x+\dfrac{5}{4})^2=\dfrac{3385}{16}$
Neglecting the negative answer, we have:
$\implies (x+\dfrac{5}{4})=14.55$
$x=13.3$ in
