Question

Completing the square X^2+8x+3=0

Answer 1

Solution by completing the square for:

2+8+3=0

x

2

+

8

x

+

3

=

0

Keep

x

terms on the left and move

the constant to the right side

by subtracting it on both sides

2+8=−3

x

2

+

8

x

=

−

3

Take half of the

x

term and square it

[8⋅12]2=16

[

8

⋅

1

2

]

2

=

16

then add the result to both sides

2+8+16=−3+16

x

2

+

8

x

+

16

=

−

3

+

16

Rewrite the perfect square on the left

(+4)2=−3+16

(

x

+

4

)

2

=

−

3

+

16

and combine terms on the right

(+4)2=13

(

x

+

4

)

2

=

13

Take the square root of both sides

+4=±13‾‾‾√

x

+

4

=

±

13

Simplify the Radical term (1):

+4=±13‾‾‾√

x

+

4

=

±

13

Isolate the x on the left side and

solve for x (1)

=−4±13‾‾‾√

x

=

−

4

±

13

therefore (2)

=−4+13‾‾‾√

x

=

−

4

+

13

=−4−13‾‾‾√

x

=

−

4

−

13

which becomes

=−0.394449

x

=

−

0.394449

=−7.60555

Answer 2

(x + 4)² - 13 = 0

Explanation:

Completing the square means to create a quadratic with the numbers that have a variable.

Here, that is x² + 8x: (x² + 8x + y²) = (x + y)².

Since 8x is the 2xy in this equation, that means 2y is 8, therefore, y is 4.

So, completing the square gives us (x + 4)² + 3 = 0.

But, because we did this, we have an extra 16 in the equation, so we have to subtract that.

That will look like: (x + 4)² - 13 = 0.