Solve quadratic equation by factoring. x2−6x+8=0

Question

Solve quadratic equation by factoring.  x2−6x+8=0

David Clayton · Accepted Answer

Step 1  Given the quadratic equation:  x2−6x+8=0  Step 2  Solving by factorization:  x2−6x+8=0  x2−4x−2x+8=0  (x2−4x)−(2x−8)=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 · Accepted Answer

In the first place, we solve the equation

x^{2} + 6 x + 8 = 0

by using the Quadratic Formula.
Recall the formula, The Quadratic Formula,
The solutions of

a x^{2} + b x + c = 0, a \neq 0

, are given by the Quadratic Formula,

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

Set a=1, b=6 and c=8.
We have

x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}

= \frac{- 6 \pm \sqrt{6^{2} - 4 (1) (8)}}{2 (1)}

= \frac{- 6 \pm \sqrt{4}}{2}

Hence we have

x = \frac{- 6 \pm \sqrt{4}}{2}

= \frac{- 6 \pm 2}{2}

Ot follows that

x = \frac{- 6 + 2}{2}

= \frac{- 4}{2}

=-2
,or

x = \frac{- 6 - 2}{2}

= \frac{- 8}{2}

=-4
In the second place, we solve

x^{2} + 6 x + 8 = 0

by factoring.
Factoring

x^{2} + 6 x + 8 = 0

, we have

x^{2} + 6 x + 8 = x^{2} + 2 x = 4 x + 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

x^{2} + 6 x + 8 = 0

is x such that
x=-4 or x=-2

alenahelenash · Accepted Answer

x2−6x+8=x2−2x−4x+8 ⇒x2−6x+8=x(x−2)−4(x−2) ⇒x2−6x+8=(x−2)(x−4) Thus, the given quadratic equation x2−6x+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, x2−6x+8=22−6∗2+8=4−12+8=0 For x=4, we get, x2−6x+8=42−6∗4+8=16−24+8=0 Result: (x-2)(x-4)=0 implies x=2 or x=4

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

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