Solve quadratic equation by factoring. x^{2}-6x+8=0

Nicontio1

Nicontio1

Answered question

2022-01-15

Solve quadratic equation by factoring.
x26x+8=0

Answer & Explanation

David Clayton

David Clayton

Beginner2022-01-16Added 36 answers

Step 1
Given the quadratic equation:
x26x+8=0
Step 2
Solving by factorization:
x26x+8=0
x24x2x+8=0
(x24x)(2x8)=0
x(x-4)-2(x-4)=0
(x-4)(x-2)=0
(x-4)=0 or (x-2)=0
x=4 or x=2
Hence, the solution is x=2,4
Marcus Herman

Marcus Herman

Beginner2022-01-18Added 41 answers

In the first place, we solve the equation x2+6x+8=0 by using the Quadratic Formula.
Recall the formula, The Quadratic Formula,
The solutions of ax2+bx+c=0,a0, are given by the Quadratic Formula,
x=b±b24ac2a
Set a=1, b=6 and c=8.
We have
x=b±b24ac2a
=6±624(1)(8)2(1)
=6±42
Hence we have
x=6±42
=6±22
Ot follows that
x=6+22
=42
=-2
,or
x=622
=82
=-4
In the second place, we solve x2+6x+8=0 by factoring.
Factoring x2+6x+8=0, we have
x2+6x+8=x2+2x=4x+8
=x(x+2)+4(x+2)
=(x+4)(x+2)
=0
Recall the property, Zero-Factor Property,
if ab=0, then a=0 or b=0. This property also applies to three or more factors.
Since (x+4)(x+2)=0, we have x+4=0 or x+2=0.
Note that x+4=0 implies x=-4.
Also, note that x+2=0 implies x=-2.
In conclusion, we obtain the solution of the equation x2+6x+8=0 is x such that
x=-4 or x=-2
alenahelenash

alenahelenash

Expert2022-01-24Added 556 answers

x26x+8=x22x4x+8 x26x+8=x(x2)4(x2) x26x+8=(x2)(x4) Thus, the given quadratic equation x26x+8=0 can be factorized as equation (x-2)(x-4)=0 which implies either x=2 or x=4. For x=2, we get, x26x+8=2262+8=412+8=0 For x=4, we get, x26x+8=4264+8=1624+8=0 Result: (x-2)(x-4)=0 implies x=2 or x=4

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