More quadratic equation help( this one I have no idea even where to start)?

Question

Here it goes: 16x^2-16x+4=0. My first step I did was factor the 4 out of that which is as follows: 4(x^2-4x+1). Is this some sort of linear equation? Cause if it is, how do I solve it? And if it is a linear equation, how do I solve it with an exponent of 2 in it?

Thank you everyone and please explain. I always need a good explaination

Answer 1

16x^2-16x+4=0.

4(4x^2 - 4x + 1) = 0

4(2x - 1)(2x - 1) = 0

This is solved when 2x-1 = 0, or x = 1/2

CHECK:
16x^2 - 16x + 4 =
16(1/2)^2 - 16(1/2) + 4 =
16(1/4) - 16(1/2) + 4 =
4 - 8 + 4 = 0

Answer 2

It is not a linear equation even if you factor out 4 because it still has a ^2 in the equation, hence it is quadratic.

To solve quadratic equations, you've got a few methods. 1) factorisation, 2) quadratic formula, 3) completing the square.

Usually use factorisation if possible, else use quadratic formula.

So your problem is
16x^2 - 16x + 4 = 0
divide by four on both sides gives,
4x^2 - 4x + 1 = 0
(2x-1)^2 = 0
x = 1/2

Hence, the solution is x = 1/2.

Answer 3

When you factored out the 4 in the quadratic equation, you should have gotten 4(4x^2 - 4x + 1) = 0; you forgot the 4 in front of the x^2. Factor out the resulting equation:
4(4x^2 - 4x + 1) = 0
4(2x-1)(2x-1) = 0

x = 0.5

Also, anything with an x^2 term is not linear; a linear equation has only x in it; not x^2 or x^3 or sqrt(x).

Answer 4

You have the right idea for the first step, which is to factor out a 4, but the coefficient that you state for the x^2 term is wrong

4x^2 - 4x + 1 = 0

Simplify the left-hand side by factoring (this takes a little practice at first, you'll get better at it with time)

4x^2 - 4x + 1 = (2x-1)(2x-1) = (2x-1)^2

(2x-1)^2 = 0

Take the square root of each side and solve:

2x -1 = 0

2x = 1 ----------> x = 1/2 or 0.5

Answer 5

4 (4x² - 4x + 1) = 0
4x² - 4x + 1 = 0
(2x - 1) (2x - 1) = 0
x = 1 / 2

Answer 6

16x^2-16x+4 = 0

divided for 16 =

x^2 - x + 4/16 = 0

(x-0.5)(x-0.5)

x - 0.5 = 0

x = 0.5