Which statement describes the first step to solve the equation by completing the square? 3x² + 18x = 21.
Multiply both sides of the equation by 19.
Add 81 to each side of the equation
Add 9 to each side of the equation
Multiply both sides of the equation by 1/3.

Solution:

Given, the equation is 3x² + 18x = 21.

We have to find the first step in solving the given equation by completing the square.

To solve the equation, first multiply by (1/3)

3x² + 18x = 21 becomes (1/3)(3x² + 18x) = 21(1/3)

We get, x² + 6x = 7

Now, x² + 6x + c = 7 --- (1)

We know, (a + b)² = a² + 2ab + b² --- (2)

Comparing (1) and (2)

a² = x²

a = x

2ab = 6x

2xb = 6x

b = 6/2

b = 3

So, c = b² = (3)² = 9

Now, x² + 6x - 7 = 0

On factoring,

x²  + 7x - x - 7 = 0

x(x + 7) - 1(x + 7) = 0

(x - 1)(x + 7) = 0

x - 1 = 0 ⇒ x = 1

x + 7 = 0 ⇒ x = -7

Therefore, the first step in solving the equation is multiplying by (1/3) on both sides.

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Which statement describes the first step to solve the equation by completing the square? 3x² + 18x = 21.

Summary:

The statement that describes the first step to solve the equation 3x² + 18x = 21 by completing the square is to multiply both sides of the equation by 1/3.