How do you solve using the completing the square method #3x^2 + 15x = 9#?

Question

Isaiah Anthony · Accepted Answer

#x=(-5+sqrt37)/2# and #x=(-5-sqrt37)/2#

To get the coefficient of #x^2# to equal 1, first divide both sides of the equation by 3.

3*(x^2)/3 + 15x)/3 = 9/3#

#x^2+5x=3#

The numerical coefficient of x is now divided by two; square the result and add it to both sides of the equation.

#3+25/4=x^2+5x+25/4#

The Perfect Square Trinomial is now as follows: #(x+5/2)^2=37/4#. Take the square root on each side.

(x+5/2)^2) = sqrt(37/4)#

#x + 5 /2 = + -1/2 sqrt(37)#

#x = -5/2 + -1/2 sqrt(37) #

There are two values.

The equations #x=-5/2+1/2sqrt(37)# and #x=-5/2-1/2sqrt(37)#

May God bless you all. I hope this explanation helps.

Kennedy Adams · Answer

undefined To solve the quadratic equation 3x^2 + 15x = 9 using the completing the square method, follow these steps:

1. Move the constant term to the right side of the equation:
   3x^2 + 15x - 9 = 0

2. Divide the entire equation by the coefficient of x^2 (in this case, 3):
   x^2 + 5x - 3 = 0

3. Add and subtract (b/2)^2 to complete the square:
   x^2 + 5x + (5/2)^2 - (5/2)^2 - 3 = 0

4. Rewrite the expression, factoring the perfect square trinomial:
   (x + 5/2)^2 - (25/4) - 3 = 0

5. Simplify:
   (x + 5/2)^2 - 25/4 - 12/4 = 0
   (x + 5/2)^2 - 37/4 = 0

6. Add (37/4) to both sides:
   (x + 5/2)^2 = 37/4

7. Take the square root of both sides:
   x + 5/2 = ±√(37/4)

8. Subtract 5/2 from both sides:
   x = -5/2 ± √(37/4)

9. Simplify the square root:
   x = -5/2 ± √37/2

Therefore, the solutions are:
   x = (-5 ± √37)/2