4.4 Introduction to quadratic equations

$x+y=0$

$\text{xy}=0$

$\text{xy}=1$

$\text{xy}>0$

OK, here’s a different sort of problem. A swimming pool is going to be built, 3 yards long by 5 yards wide. Right outside the swimming pool will be a tiled area, which will be the same width all around. The total area of the swimming pool plus tiled area must be 35 yards.

• A

  Draw the situation. This doesn’t have to be a fancy drawing, just a little sketch that shows the 3, the 5, and the unknown width of the tiled area.

• B

  Write an algebra equation that gives the unknown width of the tiled area.

• C

  Solve that equation to find the width.

• D

  Check your answer—does the whole area come to 35 yards?

$x^2+\mathrm{5x}+6=0$

${\mathrm{2x}}^2-\text{16}x+\text{15}=0$

$x^3+{\mathrm{4x}}^2-\text{21}x=0$

${\mathrm{3x}}^2-\text{27}=0$

$x^2=9$

$(x-4{)}^2=9$

$x^2-\mathrm{8x}+\text{16}=9$

$x^2-\mathrm{8x}=-7$