# How do you solve using the completing the square method #4x^2 + 4x + 1 = 49 #?

##### 3 Answers

#### Explanation:

or

and using

or

and either

or

3, and - 4

#### Explanation:

- Transforming Method

#y = 4x^2 + 4x - 48 = 0#

#y = 4(x^2 + x - 12) = 0#

Solve the quadratic equation#x^2 + x - 12 = 0# , by the new Transforming Method - case a = 1 (Socratic, Google Search)

Find 2 real roots, that have opposite signs (ac < 0), knowing the sum (-b = -1) and the product (c = -12).

They are 3 and - 4 - Completing the square method.

#4x^2 + 4x = 48#

#x^2 + x = 12#

#x^2 + x + 1/4 = 12 + 1/4 = 49/4#

#(x + 1/2)^2 = 49/4#

#x + 1/2 = +- 7/2#

#x1 = 7/2 - 1/2 = 6/2 = 3#

#x2 = - 7/2 - 1/2 = - 8/2 = - 4#

#### Explanation:

Given:

Write as:

The next step will change things in as much as it introduces a value that is not in the original equation. It is removed by introducing an as yet unknown constant of

Notice the exponent

Now we do the correction bit.

Set

Substitute into

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Add 49 to both sides

Divide both sides by 4

Square root both sides

Subtract