Question

what is completeling square method​

Answer 1

Answer:

1 ~ 8

Step-by-step explanation:

Completing the square method means,

you solve the a quadratic formula, $ax^2+bx+c=0$ like the following way :

1. $ax^2+bx+c=0$

2. $a(x^2+\frac{b}{a} x+\frac{c}{a} )=0$ ⇒ Taking $a$ Out

3. $x^2+\frac{b}{a} x+\frac{c}{a} =0$ ⇒ Dividing Both Sides By $a$

4. $x^2+\frac{b}{a} x=-\frac{c}{a}$ ⇒ Moving $\frac{c}{a}$ To Right Sand Side

5. $x^2+\frac{b}{a} x+\frac{b^2}{4a^2} =\frac{b^2}{4a^2} -\frac{c}{a}$ ⇒ Adding $\frac{b^2}{4a^2}$ To Both Sides

6. $(x+\frac{b}{2a} )^2=\frac{b^2}{4a^2} -\frac{4ac}{4a^2}$ ⇒ Using Identity To complete the square

7. $(x+\frac{b}{2a})^2 =\frac{b^2-4ac}{4a^2}$ ⇒ Simplifying Right Hand Side

8. $x+\frac{b}{2a}=\pm \sqrt{\frac{b^2-4ac}{4a^2} }$ ⇒ According To The Definition Of The Square Root

9. $x+\frac{b}{2a}=\pm\frac{\sqrt{b^2-4ac}}{2a}$ ⇒ Simplifying Right Hand Side

10 $x=\frac{-b\pm \sqrt{b^2-4ac} }{2a}$ ⇒ Moving $\frac{b}{2a}$ To Right Hand Side

Step 1 ~ 8 is 'completing the square method'.

(Quadratic formula comes from step 9 ~ 10.)

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Answer 2

Answer:

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