The document provides 5 examples of writing quadratic equations in the standard form of ax^2 + bx + c = 0. Each example expresses a given equation in terms of x and then identifies the coefficients a, b, and c. For example 1, the equation x^2 = 5 - 2x is written as x^2 + 2x - 5 = 0, with a = 1, b = 2, c = -5. The examples demonstrate how to rearrange various equations involving x terms and constants into the standard quadratic form.

1. Writing Quadratic Equation in the
Form of ax2 + bx + c = 0, and Finding
the Value of a, b, and c.

2. Example 1. x2 = 5 – 2x
ax2 + bx + c = 0
x2 = 5 – 2x
x2 + 2x – 5 = 0
a = 1, b = 2, c = -5

3. Example 2. -11x + 4 = 2x2 – x - 5
ax2 + bx + c = 0
-11x + 4 = 2x2 – x - 5
= 2x2 – x + 11x – 5 – 4 (simplify)
0 = 2x2 + 10x – 9
a = 2, b = 10, c = -9
remember: (An equation ax2 + bx + c = 0 is the same as 0 = ax2 + bx + c.)

4. Example 3. 3x2 = 36
ax2 + bx + c = 0
3x2 = 36
3x2 – 36 = 0
a = 3, b = 0, c = -36

5. Example 4. (x + 2)2 = -6 + 3x
ax2 + bx + c = 0
(x + 2)2 = -6 + 3x
x2 + 4x + 4 = -6 + 3x
x2 + 4x – 3x + 4 + 6 = 0
x2 + x + 10 = 0
a = 1, b = 1, c = 10

6. Example 5. 11 = 3x + x2
ax2 + bx + c = 0
11 = 3x + x2
0 = x2 + 3x – 11
a =1, b = 3, c = -11