Can anyone please explain how to do this? 4x^2-16x+15=0

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baxthum8 | High School Teacher | (Level 3) Associate Educator

Posted on

I'm going to safely assume the question has exponent of 2 (not written).

Solve:  `4x^2-16x + 15 = 0`

First look to factor the problem.  If factoring works, its the easiest way, otherwise use the quadratic formula.  Once we factor we'll use the zero product property.

An easy way to factor quadratic `(ax^2+bx+c)`  in which a>1: is multiply "a" and "c".

Multiply 4 x 15 = 60.

Therefore we need to find 2 numbers in which we can multiply to get 60 and add to get -16, the "b" in the quadratic.

This would be -10 and -6.

Now divide each of these by "ax" to have:

`(-10)/(4x)`  and `(-6) / (4x)`

Simplify to get `(-5)/(2x)`    and `(-3)/(2x)`

So, the original quadratic factors to:

`(2x-5) (2x - 3) = 0`

Now set each factor equal to zero and solve for x.

 `2x - 5 = 0` and  `2x - 3 = 0`

 `x = 5/2` and `x = 3/2`

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