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# How do I complete the squares on these problems?

Please help me with these three problems:

x^2-3x-28=0

x^2+6x=-41

2p^2=6p-20

How do I do these?

I need to complete the squares. Please help!

Can someone show me the work somehow?

### 4 Answers

- n00bzLv 59 years agoFavorite Answer
I can give you the first ...

x^2-3x-28=0

x^2-7x+4x-28=0

x(x-7)+4(x-7)=0

(x+4)(x-7)=0

x=-4

x=7

- 9 years ago
Problem 1:

x^2 - 3x - 28 = 0

Rewrite it as:

x^2 - 3x = 28

Add square of half of the coefficient of the middle term to both sides of equation, get:

x^2 - 3x + (-3/2)^2 = 28 + (-3/2)^2

When simplified the LHS and the RHS are:

(x - 3/2)^2 = 121/4

Therefore, the LHS is completed as a square.

Problem 2:

x^2 + 6x = -41

Add square of half of the coefficient of the middle term to both sides of equation, get:

x^2 + 6x + (6/2)^2 = -41 + (6/2)^2

i.e

x^2 + 6x + 9 = -41 + 9

Simplify both LHS and RHS

(x + 3)^2 = -32

Also, the LHS is completed as a square.

Problem 3:

2p^2 = 6p - 20

Rewrite this as:

2p^2 - 6p = -20

Divide all by 2, get:

p^2 - 3p = -10

Need to add the square of half of the coefficient of the middle term to both sides of equation, get:

p^2 - 3p + (-3/2)^2 = -10 + (-3/2)^2

By simplifying LHS and RHS differently, get:

(p - 3/2)^2 = -31/4

Check, the LHS is completed as a square.

- grandpaLv 49 years ago
x^2-3x-28=0

x^2-7x+4x-28=0

x(x-7)+4(x-7)=0

(x+4)(x-7)=0

either

x+4 =0 i.e x =-4

or x-7 =0 i.e x=7

answer x = -4 or 7

- ChrisLv 79 years ago
x^2 -3x - 28 = 0

First, push the constant to the right side by adding 28 to each side. That gets it out of the way.

x^2 - 3x = 28

Now to complete the square, take half the x coefficient, square it, and add the result to both sides.

x^2 - 3x + (-3/2)^2 = 28 + (-3/2)^2

x^2 - 3x + 9/4 = 28 + 9/4

x^2 - 3x + 9/4 = 121/4

(x - 3/2)^2 = 121/4

Now take the square root of both sides.

x - 3/2 = +/- sqrt(121/4)

x - 3/2 = +/- 11/2

x = 3/2 +/- 11/2

x = -8/2 or x = 14/2

x = -4 or x = 7

x^2 + 6x = -41

x^2 + 6x + 3^2 = -41 + 3^2

x^2 + 6x + 9 = -41 + 9

x^2 + 6x + 9 = -32

(x + 3)^2 = -32

x + 3 = +/- sqrt(-32)

x + 3 = +/- sqrt(-1 * 16 * 2)

x + 3 = +/- 4i sqrt(2)

x = -3 +/- 4i sqrt(2)

x = -3 - 4i sqrt(2) or x = -3 - 4i sqrt(2)

2p^2 = 6p - 20

p^2 = 3p - 10

p^2 - 3p = -10

p^2 - 3p + (-3/2)^2 = -10 + (-3/2)^2

p^2 - 3p + 9/4 = -10 + 9/4

(p - 3/2)^2 = -31/4

p - 3/2 = +/- sqrt(-31/4)

p = 3/2 +/- sqrt(-1 * 31) / 2

p = 3/2 +/- i sqrt(31) / 2

p = 3/2 + i sqrt(31) or p = 3/2 - i sqrt(31)