**Solving Word Problems Involving Quadratic Equations:**

Many algebraic word problems involve quadratic equations. The algebraic expressions any time describing the relationships in the problem involve a quantity multiplied by it; a quadratic equation must be used to solve the problem. The steps for solving word problems involving quadratic equations are the same as for solving word problems involving linear equations.

**Example:**

A radiation control point is set up near a solid waste disposal facility. The pad on that the facility is set up measures 20 feet by 30 feet. If a health physicist sets up a controlled walkway around the pad that reduces the area by 264 square feet, how huge is the walkway?

**Solution:**

**Step 1**. Let x = Width of the Walkway

**Step 2.** Then,

30 - 2x = Length of Reduced Pad

20 - 2x = Width of Reduced Pad

**Step 3. **Area of Reduced Pad = (Length of Reduced Pad)(Width of Reduced Pad)

600 - 264 = (30 - 2x)(20 - 2x)

336 =600 - 100x + 4x^{2}

**Step 4**. Solve this quadratic equation.

4x^{2} - 100x + 264 = 0

By using the Quadratic Formula, substitute the coefficients for a, b, and c and solve for x.

X = 100 ± 76 /8

X = 100+ 76/8, 100- 76 /8

X = 176/8, 24/8

X = 22, 3

The two roots are x = 22 feet and x = 3 feet. Here x = 22 feet is not physically useful, the answer is x = 3 feet.

**Step 5. **Check the answer.

The area of the decreased area pad is 264 square feet less than the area of the original pad.

600 - 264 = (20 - 2x)(30 - 2x)

336 = [20 - 2(3)][30 - 2(3)]

336 = (20 - 6)(30 - 6)

336 = (14)(24)

336 = 336

Therefore, the answer checks.