Help on solving equation 2x^2 - 3x + 1

[destiny_deity]

There are three ways to solve a equation like this:

2x^2-3x+1

I need help combining the square on this certain equation.

 

[tkhunny]

1) It's not an equation. Do you see one of these: "="?
2) It's COMPLETING the Square.

This is the foundation

(a+b)^2 = a^2 + 2ab + b^2

y = 2x^2 - 3x + 1

Factor out the leading coefficient from the first two terms.

y = 2(x^2 - (3/2)x) + 1

Leave lots of room forr a couple of magic numbers

y = 2(x^2 - (3/2)x + ______) + 1 - 2(______)

It's inside the parentheses, so the Distributive Property of Multiplication over Addition makes us multiply it by 2.

Calculate the magic number:

(3/2)/2 = 3/4
(3/4)^2 = 9/16

Fill in the blanks

y = 2(x^2 - (3/2)x + 9/16) + 1 - 2(9/16)

Simplify

y = 2(x - (3/4)x)^2 + 1 - (9/8)
y = 2(x - (3/4)x)^2 - (1/8)

Now what?

 

[destiny_deity]

1) It's not an equation. Do you see one of these: "="?
2) It's COMPLETING the Square.

This is the foundation

(a+b)^2 = a^2 + 2ab + b^2

y = 2x^2 - 3x + 1

Factor out the leading coefficient from the first two terms.

y = 2(x^2 - (3/2)x) + 1

Leave lots of room forr a couple of magic numbers

y = 2(x^2 - (3/2)x + ______) + 1 - 2(______)

It's inside the parentheses, so the Distributive Property of Multiplication over Addition makes us multiply it by 2.

Calculate the magic number:

(3/2)/2 = 3/4
(3/4)^2 = 9/16

Fill in the blanks

y = 2(x^2 - (3/2)x + 9/16) + 1 - 2(9/16)

Simplify

y = 2(x - (3/4)x)^2 + 1 - (9/8)
y = 2(x - (3/4)x)^2 - (1/8)

Now what?

Thanks a bunch for helping me out... I sometimes do typos cuz I type fast.

 

[tkhunny]

Here's a plan, slow down. Learn from your errors, don't excuse them.