8/9 (54x - 36) + 2 = -3/4(-40 + 16x) + 90x. Solve for x

1 answer:

7 0

$\dfrac{8}{9}(54x-36)+2=-\dfrac{3}{4}(-40+16x)+90x\ \ \ \ |\text{use distributive property}\\\\\dfrac{8}{9}(54x)-\dfrac{8}{9}(36)+2=-\dfrac{3}{4}(-40)-\dfrac{3}{4}(16x)+90x\\\\8\cdot6x-8\cdot4+2=3\cdot10-3\cdot4x+90x\\\\48x-32+2=30-12x+90x\ \ \ \ |\text{simlify}\\\\48x-30=30+78x\ \ \ \ |+30\\\\48x=60+78x\ \ \ \ \ |-78x\\\\-30x=60\ \ \ \ |:(-30)\\\\\boxed{x=-2}$

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1. What values of a, b, and c would you use in the quadratic formula for the following equation?

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Question (1):
The general formula of the quadratic equation is:
ax² + bx + c = 0
The given equation is:
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Rearrange the given equation to look the standard one:
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Now, compare the coefficients in the given equation with the standard one, you will find that:
a = 5, b = 9 and c = -4

Question (2):
The given expression is:
-5 + 2x² = -6x
Rearrange this expression to be in standard form:
2x² + 6x - 5 = 0
This means that:
a = 2
b = 6
c = -5
The roots of the equation can be found using the formula in the attached image.
Substituting in this formula with the given a, b and c, we would find that the correct choice is third one (I have attached the correct choice)

Question (3):
Quadratic formula (the one used in the previous question, also shown in attached images) is the best method to get the solution of any quadratic equation. This is because, putting the equation in standard form, we can simply get the values of a, b and c, substitute in the formula and get the precise solutions of the equation.

Hope this helps :)