Question

Gio is solving the quadratic equation by completing the square. 5x2 + 15x – 4 = 0. What should Gio do first

Answer 1

Answer: A

Step-by-step explanation:

The correct answer is the first option which is to isolate the constant. Completing the square is done as follows:

1. Write the equation in a way that the constants are in the right side while the terms with x are on the left. 

5x2 + 15x  = 4

2. Make sure that the coefficient of the x^2 term is 1.

5(x^2 + 3x)  = 4

3. Adding a term to both sides that will complete the square in the left side. This is done by dividing the coefficient of the x term by 2 and squaring it. Note: The same amount should be added to the right side to balance the equation.

5(x^2 + 3x + 9/4)  = 4 +45/4

5(x+3/2)^2 = 61/4

Answer 2

We observe that we have a polynomial of the form:
 ax2 + bx + c
 Therefore, to complete the square, we must use the following formula:
 a (x + (b / 2a)) ^ 2 + c - (b ^ 2 / 4a)
 Thus,
 Step 1: 
 We define:
 a = 5
 b = 15
 c = -4
 Step 2: 
 we use the formula:
 5 (x + (15 / (2 * 5))) ^ 2 + (-4) - ((15) ^ 2 / (4 * 5))
 5 (x + (15 / (2 * 5))) ^ 2 - 15.25
 5 (x + 1.5) ^ 2 - 15.25

 5 (x + 3/2) ^ 2 - 61/4

 Answer:
 Gio should do first: 
 a (x + (b / 2a)) ^ 2 + c - (b ^ 2 / 4a)
 a = 5
 b = 15 
 c = -4