Question

Which statement describes the first step to solve the equation by completing the square? 3x^2 + 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 13 .

Answer 1

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

The factors of the equations 3x²+ 18x= 21 are 1 ,-7 .

Explanation:

As given the equations

3x² + 18x = 21

Multiply both sides of the equation by
`(1)/(3)`.

Thus the equation becomes

`(3x^(2)+18x)*(1)/(3) =21* (1)/(3)`

Simplify the above

x² + 6x = 7

Adding 9 on both sides of the above equation

x² + 6x + 9 = 7 + 9

x² + 6x + 9 = 16

(As (a +b)² = a² + b² + 2ab

Thus (x+3)² = x² + 6x + 9 )

Put in the above

(x+3)² = 16

Taking square root on both side

`\sqrt{(x+3)^(2)} = √(16)`

√16 = ± 4

`\sqrt{(x+3)^(2)} = (x+3)`

First take

(x + 3) = 4

x = 4 -3

x = 1

Second take

(x+ 3) = -4

x = - 4 -3

x = -7

Therefore the first step to solve the equation by completing the square 3x²+ 18x= 21 is multiply both sides of the equation by
`(1)/(3)`.

The factors of the equations 3x²+ 18x= 21 are 1 ,-7 .