Answer:
The first step to solve the equation by completing the square 3x²+ 18x= 21 is multiply both sides of the equation by \(\frac{1}{3}\).
The factors of the equations 3x²+ 18x= 21 are 1 ,-7 .
Step-by-step explanation:
As given the equations
3x² + 18x = 21
Multiply both sides of the equation by \(\frac{1}{3}\).
Thus the equation becomes
\((3x^{2}+18x)\times\frac{1}{3} =21\times \frac{1}{3}\)
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
\(\sqrt{(x+3)^{2}} = \sqrt{16}\)
√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 \(\frac{1}{3}\).
The factors of the equations 3x²+ 18x= 21 are 1 ,-7 .
