Solve this by completing square method please?

Question

1. x^2 + 4x - 1085 = 0
2. x^2 - x - 1806 = 0
3. 2x^2 + 12x - 110 = 0

Answer 1

i will do one of these.

1) x2 + 4x - 1085 = 0

x2 + 4x + 4 - 1085 = 4
(x+2)^2 -1085 = 4
(x+2)^2 = 1089, take sqrt of both sides. there will be 2 solutions

x+2 = +- 33
x = 31
x = -35

so x = 31 or x = -35

Answer 2

The basic method is to take the middle x-coefficient and dividing it by 2, then squaring it. Using this magic number, you can add it to both sides and factor the binomial.

1. The magic number: 4

Then you add 4 to both sides and factor the binomial:
x2 + 4x + (4) - 1085 = (4)
(x + 2)^2 - 1085 = 4
(x + 2)^2 = 1089

x = 31 and x = -35

2. The magic number: 1/4

x2 - x + (1/4) - 1806 = (1/4)
(x - 1/2)^2 - 1806 = 1/4
(x - 1/2)^2 = 1806 1/4

x = 43 and x = 42.

3. You should factor 2 out of the equation first.
x2 + 6x - 55 = 0

The magic number: 9

x2 + 6x + (9) - 55 = (9)
(x + 3)^2 - 55 = 9
(x + 3)^2 = 64

x = 5 and x = -11

Answer 3

Question 1
(x² + 4x + 4) - 4 - 1085 = 0
(x + 2)² = 1089
(x + 2) = ± √1089
x + 2 = ± 33
x = 31, x = - 35
Question 2
(x² - x + 1/4) - 1/4 - 1806 = 0
(x - (1/2)²) = 1/4 + 7224 / 4
(x - (1/2)²) = 7225/4
(x - (1/2)) = ± 85 / 2
x = (1/2) ± 85/2
x = 86/2 , x = - 84 /2
x = 43, x = - 42
Question 3
x² + 6x - 55 = 0
(x² + 6x + 9) - 9 - 55 = 0
(x + 3)² = 64
(x + 3) = ± 8
x = 5 , x = - 11

Answer 4

-------2.------
Simplifying
x2 + -1x + -1806 = 0

Reorder the terms:
-1806 + -1x + x2 = 0

Solving
-1806 + -1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1806' to each side of the equation.
-1806 + -1x + 1806 + x2 = 0 + 1806

Reorder the terms:
-1806 + 1806 + -1x + x2 = 0 + 1806

Combine like terms: -1806 + 1806 = 0
0 + -1x + x2 = 0 + 1806
-1x + x2 = 0 + 1806

Combine like terms: 0 + 1806 = 1806
-1x + x2 = 1806

The x term is -1x. Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 1806 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 1806 + 0.25

Combine like terms: 1806 + 0.25 = 1806.25
0.25 + -1x + x2 = 1806.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 1806.25

Calculate the square root of the right side: 42.5

Break this problem into two subproblems by setting
(x + -0.5) equal to 42.5 and -42.5.

Subproblem 1
x + -0.5 = 42.5

Simplifying
x + -0.5 = 42.5

Reorder the terms:
-0.5 + x = 42.5

Solving
-0.5 + x = 42.5

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = 42.5 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 42.5 + 0.5
x = 42.5 + 0.5

Combine like terms: 42.5 + 0.5 = 43
x = 43

Simplifying
x = 43

Subproblem 2
x + -0.5 = -42.5

Simplifying
x + -0.5 = -42.5

Reorder the terms:
-0.5 + x = -42.5

Solving
-0.5 + x = -42.5

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '0.5' to each side of the equation.
-0.5 + 0.5 + x = -42.5 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -42.5 + 0.5
x = -42.5 + 0.5

Combine like terms: -42.5 + 0.5 = -42
x = -42

Simplifying
x = -42

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {43, -42}

-------3.--------
Simplifying
2x2 + 12x + -110 = 0

Reorder the terms:
-110 + 12x + 2x2 = 0

Solving
-110 + 12x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-55 + 6x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-55 + 6x + x2)' equal to zero and attempt to solve:

Simplifying
-55 + 6x + x2 = 0

Solving
-55 + 6x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '55' to each side of the equation.
-55 + 6x + 55 + x2 = 0 + 55

Reorder the terms:
-55 + 55 + 6x + x2 = 0 + 55

Combine like terms: -55 + 55 = 0
0 + 6x + x2 = 0 + 55
6x + x2 = 0 + 55

Combine like terms: 0 + 55 = 55
6x + x2 = 55

The x term is 6x. Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = 55 + 9

Reorder the terms:
9 + 6x + x2 = 55 + 9

Combine like terms: 55 + 9 = 64
9 + 6x + x2 = 64

Factor a perfect square on the left side:
(x + 3)(x + 3) = 64

Calculate the square root of the right side: 8

Break this problem into two subproblems by setting
(x + 3) equal to 8 and -8.

Subproblem 1
x + 3 = 8

Simplifying
x + 3 = 8

Reorder the terms:
3 + x = 8

Solving
3 + x = 8

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + x = 8 + -3

Combine like terms: 3 + -3 = 0
0 + x = 8 + -3
x = 8 + -3

Combine like terms: 8 + -3 = 5
x = 5

Simplifying
x = 5

Subproblem 2
x + 3 = -8

Simplifying
x + 3 = -8

Reorder the terms:
3 + x = -8

Solving
3 + x = -8

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + x = -8 + -3

Combine like terms: 3 + -3 = 0
0 + x = -8 + -3
x = -8 + -3

Combine like terms: -8 + -3 = -11
x = -11

Simplifying
x = -11

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5, -11}
Solution
x = {5, -11}