Question

If using the method of completing the square to solve the quadratic equation
x2 + 5x – 21 = 0, which number would have to be added to "complete the
square"?

Answer 1

Answer:

Step-by-step explanation:

ax² + bx + c = y

x² + 5x – 21 = 0

First make sure the (a) term = 1... It is.

Get (c) to zero or blank by adding or subtracting as needed.

x² + 5x – 21 + 21 = 0 + 21

x² + 5x       = 21

Add the square of half of the b term to each side

x² + 5x + (5/2)² = 21 + (5/2)²

x² + 5x + (5/2)² = 27.25

rewrite the left side as a square

(x + 2.5)² = 27.25

square root of each side

x + 2.5 = ±√27.25

isolate x

x = -2.5 ±√(27.25)

x ≈ 2.72 or -7.72

Answer 2

Answer:

$\frac{25}{4}$ = 6.25

Step-by-step explanation:

x² + 5x - 21 = 0 ( add 21 to both sides )

x² + 5x = 21

To complete the square

add ( half the coefficient of the x- term )² to both sides

x² + 2($\frac{5}{2}$ )x + $\frac{25}{4}$ = 21 + $\frac{25}{4}$

(x + $\frac{5}{2}$ )² = $\frac{109}{4}$