Question

The first two steps in the derivation of the quadratic formula by completing the square are shown below.
Which answer choice shows the correct next step?
Step 1: ax^2+ bx+c = 0
Step 2: ax^2 + bx=-c

Answer 1

Answer:

The correct next step is the answer choice

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

Step-by-step explanation:

we have the quadratic equation in standard form

$ax^{2}+bx+c=0$

The steps in the derivation of the quadratic formula by completing the square are

step 1

$ax^{2}+bx+c=0$ ----> given equation  

step 2

Move the constant term over to the right-hand side

$ax^{2}+bx=-c$

step 3

The leading term is multiplied by a

so

Divide by a both sides

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

step 4

Multiply the linear term by 1/2

$\frac{b}{a}(\frac{1}{2})=+\frac{b}{2a}$

step 5

square this derived value

$+\frac{b^2}{4a^2}$

step 6

Add this squared value to either side of the equation

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

step 7

convert to the common denominator, and combine on the right-hand side

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

step 8

convert the left-hand side to completed-square form

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

step 9

take the square roots of either side

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

step 10

solving for the variable

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

Answer 2

Answer:

C on edge

Step-by-step explanation: