Algebraic Equation

Question

Solve by completing the square 5𝑥2 − 4𝑥 + 2 = 0

Answer 1

To complete the square, the leading term as to be 1, so for 5x² - 4x + 2 = 0, the first step is to divide every term by the 5. At the same time, go ahead and subtract the constant, so that it's on the other side of the equation.

x² - (4/5)x = -2/5

The process of completing the square takes the quadratic expression and turns it into a perfect square. To do that, you need to take half of the "b" term's coefficient, then square it and add it to both sides of the equation. Our "b" coefficient in -4/5, half of that is -2/5, and the square that is 4/25. Add that to both sides of the equation, and you'll get:

x² - (4/5)x + 4/25 = -2/5 + 4/25

Now rewrite the left side into a perfect square and combine the two constants on the right side:

(x - 2/5)² = -6/25

Square root both sides, but don't forget to use the ± when you square root the constant on the right side.

x - 2/5 = ±√(-6/25)

Simplify and add the -2/5 on both sides to get the final answer. For the square root of a negative, we will need to use the imaginary unit, i.

x = 2/5 ± i√(6)/5

or x = (2 ± i√6)/5

Answer 2

Hello, thank you for posting your question!

The first step to answering this one if it wants you to do it by completing the square would be factoring out the 5

5(x^2 – 4/5x ) = -2

(x^2 – 4/5x ) = -2/5

The term that you add to both sides then would be (-4/5 / 2)^2 = 4/25

(x^2 – 4/5x + 4/25) = -2/5 + 4/25

(x – 2/5)^2 = -6/25

So that finishes off the portion of this that is completing the square! Once you have it to here you can just solve it algebraically! Meaning take the square root of both sides and then solve for the value of x

I hope that helps get you moving in the right direction! Feel free to reach out if you have any more questions beyond that :)

Answer 3

5x^2 -4x + 2 = 0

5(x^2 -4x/5) = -2

5(x^2 -4x/5 + 4/25) = -2 + 4/5

5(x-2/5)^2 = -6/5

(x-.4)^2 = -6/25

x-.4 = +/-(I/5)sqr6

x = .4 +/-.2isqr6

completing the square is for squares (see the movie pulp Fiction as she calls John Travolta a square)

best is factor if you can

then use the quadratic formula if you can't factor

check by graphing and find the x intercepts = the real solutions

Answer 4

5x² - 4x + 2 = 0

5x² - 4x = -2

x² - (4/5)x = -2/5

Add [(1/2)(-4/5)]² to both sides to get: x² - (4/5)x + 4/25 = -2/5 + 4/25

(x - 2/5)² = -6/25

x - 2/5 = ± √(-6/25)

x = {2 ± √6 i) / 5