Choose a method (factoring. square root property, completing the square, and the quadratic formula) to solve each of the following quadratic equations.
each method can be used only once
a) 4x2 – 27 = 0
b) 4x2 – 8x – 5 = 0
c) 4x2 – 8x – 12 = 0
d) 4x2 – 9x – 7 = 0

Part A)

Part B)  and

Part C)  and

Part D)  and

Step-by-step explanation:

Part A) we have

we know that      

The square root property states that if we have an equation with a perfect square on one side and a number on the other side, then we can take the square root of both sides and add a plus or minus sign to the side with the number and solve the equation.

isolate the term that contains the squared variable

take the square root of both sides

simplify

Part B) we have

Using the quadratic equation  

The formula to solve a quadratic equation of the form

is  

in this problem we have

so

substitute in the formula

Part C) we have

Using Factoring  

Simplify the expression first

Divide by 4 both sides

Find two numbers a and  b such that

a+b=-2

ab=-3

Solve the system by graphing

The solution is a=1, b=-3  

see the attached figure

so

The solutions are

Part D) we have

Solve by completing the square

Group terms that contain the same variable, and move the constant to the opposite side of the equation

Factor the leading coefficient

Complete the square. Remember to balance the equation by adding the same constants to each side

Rewrite as perfect squares

take square root both sides