Respuesta :
Answer:
Logical first step: divide everything by
3
Explanation:
→
x
2
−
8
x
+
8
=
0
Completing the square would mean: taking half of the
x
-coefficient and squaring that:
x
2
−
8
x
+
(
−
4
)
2
=
x
2
−
8
x
+
16
=
(
x
−
4
)
2
But we still have to balance the
16
with the
8
we had:
→
x
2
−
8
x
+
16
→(x−4)2−8=0→(x−4)2=8
So
x-4=√8=2√2→x=4+2√2
Or
x−4=−√8=−2√2→x=4−2√2
Often written as x1,2=4±2√2
The solution of the given quadratic equation by completing the square method are [tex]2\sqrt{6} -4 \ or -2\sqrt{6} -4[/tex].
What is completing the square method?
Completing the square method is factorizing a quadratic equation, and henceforth finding the roots or zeros of a quadratic polynomial or a quadratic equation.
According to the given question.
We have a quadratic equation
[tex]3x^{2} + 24x - 24 = 0[/tex]
The above quadratic equation can be written as
[tex]3(x^{2} + 8x - 8) = 0[/tex]
[tex]\implies x^{2} + 8x -8= 0[/tex]
Now, we will solve the above equation by completing the square method.
[tex]x^{2} +8x - 8= 0[/tex]
[tex]\implies x^{2} + 2(4x) +(4)^{2} -(4)^{2} -8 = 0[/tex]
[tex]\implies x^{2} + 2(4x) + 16 - 16 -8 = 0[/tex]
[tex]\implies (x+4)^{2} - 24=0[/tex]
[tex]\implies (x+4)^{2} = 24[/tex]
[tex]\implies (x+4)^{2} = 24[/tex]
[tex]\implies (x+4) = \sqrt{24}[/tex]
[tex]\implies x+ 4 = \pm 2\sqrt{6}[/tex]
[tex]\implies x = 2\sqrt{6} -4 \ or -2\sqrt{6} -4[/tex]
Hence, the solution of the given quadratic equation by completing the square method are [tex]2\sqrt{6} -4 \ or -2\sqrt{6} -4[/tex].
Find out more information about completing the square method here:
https://brainly.com/question/26107616
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