Question

Fill in the missing steps for the derivation of the

quadratic formula using the choices below.

Step 1: ax? + bx + c = 0

Step 2: ax? + bx = -c

Step 3:

2a

Aix + = +V02-4ac

B: x2 + x

Step 4: x2 + x +

= =+ b

40-

Step 5:

Step 6:

- b + Vb2 - 4ac

- za

Step 7 x = - + Vo? Z4ac

D: (x+3)* = -ae. b?

Step 8:

Step 8

DONE

DONE

.

Answer 1

Answer:

step 1: $ax^2$+bx+c=0

step 2:$ax^2+bx=-c$

step 3: $x^2+\frac{b}{a}x=\frac{-c}{a}$

step 4:$x^2+(\frac{b}{2a})^{2} =\frac{b}{2a}) ^{2} \frac{-c}{a}$

step 5: $(x+\frac{b}{2a} )^{2} =\frac{b^2-4ac}{4a^2}$

step 6:$x=\sqrt{\frac{b^2-4ac}{4a^2} }$

step 7: $x=\sqrt{\frac{b^2-4ac}{2a}$

Step-by-step explanation:

from step 6 there should be a plus and minus sign before the square root.

Answer 2

The given expression for x is $x = { \frac{-b\pm\sqrt{b^2-4ac} }{2a}}$

Given the quadratic expression $ax^2 + bx+ c = 0$

We are to make x the subject of the formula using the completing the square method

Step 1: Given the equation $ax^2 + bx+ c = 0$

Step 2: Subtract c from both sides

$ax^2+bx+c-c = 0-c\\ax^2+bx = -c$

Step 3: Divide through by a:

$\frac{ax^2}{a} + \frac{b}{a} x= \frac{-c}{a} \\x^2 +\frac{b}{a} x=\frac{-c}{a}$

step 4: Add the square of half of the coefficient of x to both sides:

$\\x^2 +\frac{b}{a} x + (\frac{b}{2a} )^2=\frac{-c}{a} + (\frac{b}{2a} )^2\\ \\x^2 +\frac{b}{a} x + \frac{b^2}{4a^2} =\frac{-c}{a} + \frac{b^2}{4a^2} \\(x+\frac{b}{2a} )^2 = \frac{-c}{a} + \frac{b^2}{4a^2}$

Step 5: Find the LCM

$(x+\frac{b}{2a} )^2 = \frac{-4ac+b^2}{4a^2} \\(x+\frac{b}{2a} )^2 = \frac{b^2-4ac}{4a^2}$

Step 6: Square root both sides:

$\sqrt{(x+\frac{b}{2a} )^2} =\sqrt{ \frac{b^2-4ac}{4a^2}} \\x+\frac{b}{2a} =\pm\sqrt{ \frac{b^2-4ac}{4a^2}} \\x = -\frac{b}{2a} \pm{ \frac{\sqrt{b^2-4ac} }{2a}}$

Step 7: Simplify to get the value of x

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

This given the required value of x

Learn more here: https://brainly.com/question/24018325