# Solving a hard algebraic equation

The question is:

Rectangular floor mats have an area of $x^2 + 2x - 15 \text{ cm}^2$. The length is $x + 5\text{ cm}$, and the width is $100\text{ cm}$. How do I find out the value of $x$, and from there the length of the mat? The equation to find the width is $$\frac{x^2+2x-15}{\text{length}}$$

• Can you factor $x^2+2x-15$? – Ghartal Jul 4 '16 at 8:08
• Area of rectangle $=$ length $\times$ width. Use that and solve the quadratic equation. – John_dydx Jul 4 '16 at 8:09
• There isn't a quadratic equation involved in this I believe John – Kiwi Jul 4 '16 at 8:12
• @Kiwi You are right, see my hint. – Olivier Oloa Jul 4 '16 at 8:16

Hint. One may solve, for $x>0$, $$\frac{x^2+2x-15}{x+5}=100$$ or $$\frac{(x+5)(x-3)}{x+5}=100$$
• @Kiwi We have $x^2+2x-15=(x^2+2x+1)-16=(x+1)^2-4^2=[(x+1)-4][(x+1)+4]=(x-3)(x+5)$. – Olivier Oloa Jul 4 '16 at 8:20