I would be able to do problem if the 4 had a x but i cant breakdown otherwise
I am having a problem solving 2x^2-9x+4
There is no need to assume the expression is equal to zero.
Instead assuming the expression is equal to an unknown y will be your best analytical guide for future advanced math classes including calculus.
2x^2 - 9x + 4 is factorable to (2x-1)(x-4) as my fellow tutors have already expounded upon.
Analytically, it's an upward parabola since there is a positive x^2 included in the expression.
If the base of the parabola is above the x axis then, then y will never equal zero so bad bad bad assumption.
Calculus is your best analytical tool. When you calculate dy/dx and set the result equal to zero, you will find the x value of the base of the parabola.
dy/dx = (4x - 9) = 0, and thus the line x = 2.25 sits on the extreme base of the upward parabola.
When y = (2x-1)(x-4) and you plug in x, you'll get y = (3.5)(-1.75) = -6.125
So the base of the parabola is located at (2.25, -6.125) where the y value of the upward parabola's extreme base is below the x axis.
Only now can you conclude there are two points on y where the parabola touches the x-axis.
There are an infinite many points along the parabola, but x = 4 and x = 1/2 when y = 0 are usually of interest.
I intentionally do not say 'or', but rather I say 'and' because of definitive conclusion there are two points where the parabola touches the x-axis (also known as when y = 0)
This problem is factorable since 2*4 = (-1)(-8), and (-1) + (-8) = -9.
2x^2-9x+4 = (2x-1)(x-4) = 0
x = 1/2, 4 <==Answer
The expression you have given is not an equation (does not equal something), so it cannot be solved. I am going to assume that the expression is supposed to equal zero, and then solve that equation.
The equationthat I am going to solve is 2x2 - 9x + 4 = 0. The method I am going to use is called completing the square.
2x2 - 9x + 4 = 0
2x2 - 9x + 4 -4 = 0 -4 Subtract 4 from each side
2x2 - 9x = -4 Simplify
(2x2 - 9x)/x = -4/2 Divide both sides by two (the coefficient of x2)
x2 -9/2*x = -2 Distribute on the left, simplify the right
x2 - 9/2*x + 81/16 = -2 + 81/16 Add 81/16 to each side (divide the coefficient on x by two, then square
(x - 9/4)2 = -2 + 81/16 Factor the left side as a perfect square (9/4 is the square root of
(x - 9/4)2 = -32/16 + 81/16 Change the fractions on the right so that they have common
(x - 9/4)2 = 49/16 Simplify
x - 9/4 = +/- sqrt(49/16) Take the square root of both sides (sqrt means square root)
x - 9/4 = +/- 7/4 Simplify
x - 9/4 = 7/4 or x -9/4 = -7/4 Separate the problem into positive and negative values on the right
x - 9/4 + 9/4 = 7/4 +9/4 or Add 9/4 to both sides on both possible solutions
x - 9/4 + 9/4 = -7/4 + 9/4
x = 16/4 or x = 2/4 Simplify each solution
x = 4 or x = 1/2 Reduce the fractions
Completing the square is a valuable tool to use, because any binomial equation can be solved with it. Even though you could find the answer to this problem without it, I wanted to give you a chance to learn how to use it.