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:
(x + 4)² - 13 = 0
Step-by-step 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.
