Completing the square?

Question

Solve by completing the square

x^2-14x+45=0

Answer 1

[02]
x^2-14x+45=0
x^2-14x= -45
(x)^2-2*x*7+(7)^2= -45+49 [adding 7^2 or 49 to both sides]
(x-7)^2=4
x-7=+-2 [square-ooting both sides]
x=7+-2=9 or 5

Answer 2

Simplifying
x^2 + -14x + 45 = 0

Reorder the terms:
45 + -14x + x^2 = 0

Solving
45 + -14x + x^2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-45' to each side of the equation.
45 + -14x + -45 + x^2 = 0 + -45

Reorder the terms:
45 + -45 + -14x + x^2 = 0 + -45

Combine like terms: 45 + -45 = 0
0 + -14x + x^2 = 0 + -45
-14x + x^2 = 0 + -45

Combine like terms: 0 + -45 = -45
-14x + x^2 = -45

The x term is -14x. Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x^2 = -45 + 49

Reorder the terms:
49 + -14x + x^2 = -45 + 49

Combine like terms: -45 + 49 = 4
49 + -14x + ^2 = 4

Factor a perfect square on the left side:
(x + -7)(x + -7) = 4

Calculate the square root of the right side: 2

Break this problem into two subproblems by setting
(x + -7) equal to 2 and -2.

Subproblem 1
x + -7 = 2

Simplifying
x + -7 = 2

Reorder the terms:
-7 + x = 2

Solving
-7 + x = 2

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = 2 + 7

Combine like terms: -7 + 7 = 0
0 + x = 2 + 7
x = 2 + 7

Combine like terms: 2 + 7 = 9
x = 9

Simplifying
x = 9

Subproblem 2
x + -7 = -2

Simplifying
x + -7 = -2

Reorder the terms:
-7 + x = -2

Solving
-7 + x = -2

Solving for variable 'x'.

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

Add '7' to each side of the equation.
-7 + 7 + x = -2 + 7

Combine like terms: -7 + 7 = 0
0 + x = -2 + 7
x = -2 + 7

Combine like terms: -2 + 7 = 5
x = 5

Simplifying
x = 5

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9, 5}

Answer 3

x^2 - 14x + 45 = 0
x^2 - 14x = -45
x^2 - 14x + 49 = 4
(x - 7)^2 = 4
x - 7 = +/- sqrt(4)
x = +/- sqrt(4) + 7
x = 2 + 7 or x = -2 + 7
x = 5 or x = 9
x Є {5, 9}

Answer 4

for a square: (x+a)^2 = x^2+2ax+a^2
here a = 7 => a^2 should be 49.
Thus writing 45 as 49-4 we get
x^2+(2*7*x)+(7*7) - 4 = 0
=> (x-7)^2 = 4
=> (x-7) = +/- 2
=> x= 7+2=9 or 7-2=5

Answer 5

What completing the square means is making the left side of the equation into a square in the form of (Ax + B)^2 or A^2x +2ABx + B^2 form. This done by adding to the right side. This gives a positive and negative result on the right side when you take the square root of both sides..
In this case A=1 B =-7 . See this in raven's work above.

Answer 6

(x² - 14x + 49) = 49 - 45
(x - 7)² = 4
(x - 7) = ± 2
x = 9 , x = 5

Answer 7

x^2-14x+49-49+45=0
(x-7)^2-4=0
x-7=+-2
x=5,9

Answer 8

( x-5)(x-9)=0

x=5 x=9