4x^2 - 6 + -2x^2 + 19 x =180?

Question

please explain the process

Answer 1

First combine all the terms to one side, thereby setting the equation equal to zero.
2x^2 + 19x -186 = 0

Note 6 * 31 = 186, so this equation factors nicely to
(2x + 31)(x - 6)
By the Zero factor property (if ab=0, then either a=0 or b=0)
we get
2x+31 = 0 or x-6 = 0
So x=-31/2 or x=6, or in set notation x={31/2, 6}

Answer 2

I don't know exactly what you are asking but if you are asking what x is supposed to be then hopefully this will help.
Combine like terms which means any x that has a power on it gets added to the other x's with the same power. So in this case 4x^2 + -2x^2 = 2x^2 because all you do is add coefficients.
Then, set the whole thing equal to zero which means that you need to move the 180 over to the other side by subtracting it (because it is positive) from both sides of the equal sign. So you get:
2x^2 + 19x -186 = 0
Then, use the quadratic formula to solve for x by using the fact that the coefficient of the squared term is "a", the coefficient of the single x is "b" and the constant (-186) is "c".
This is the quadratic formula:
[-b +/- sqrt(b^2 - 4ac)]/2a
The opposite of b plus or minus the square root of b squared minus 4 times a times c and all of that over 2 times a.
So,
[-19 +/- sqrt(19^2 - 4(2)(-186))]/[(2)(2)] = x
Which gives you,
(-19 +/- 43)/4 = x
so x = 6 and -15.5
There you have it!!

Answer 3

4 -2 = 2
-180 - 6 = - 186
4x^2 - 6 + -2x^2 + 19 x = 180
2x^2 + 19x -186 = 0

Use the quadratic equation to solve for x: a =2, b = 19, c = -186

Answer 4

4x^2 - 6 + -2x^2 + 19 x = 180
First combine like terms
2x^2 + 19x - 6 = 180
Subtract 180 from each side
2x^2 + 19x - 186 = 0
Now factor.
(x-6)(2x+31) = 0
x - 6 = 0 or 2x +31 = 0
x = 6 or x = -31/2 = -15.5
Answer: x = -15.5 or 6

Answer 5

4x^2 - 6 + -2x^2 + 19 x =180
(4x^2 - 2x^2) + 19x - 6 - 180 = 0
2x^2 + 19x - 186 = 0
(-2x - 31)*(-x + 6) = 0

case 1
-2x - 31 = 0 therefore x = - 31/2
case 2
-x + 6 = 0 therefore x = 6

So x = -15.5 or 6

Answer 6

you can either factor or use the quadratic formula

4x^2-6-2x^2+19x=180 combine like terms and set equal to 0
2x^2+19x-186=0 now you can factor
(x-6)(2x+31)=0 set each term equal to zero

(x-6)=0 (2x+31)=0
x=6
(2x+31)=0
2x = -31
x= -31/2

quadratic formula

x=(-b+sqrtb^2-4ac)/ 2a where a=2, b=19, c=-186

x=(-19+sqrt19^2-4(2)(-186))/ (2(2) )

X=6

x=(-19-sqrt19^2-4(2)(-186))/(2(2) )

x=-31/2

check plug back into original equation

4(6)^2-6-2(6)^2+19(6)=180 true

4(-31/2)^2-6-2(-31/2)^2+19(-31/2)=180 true

Answer 7

4x^2-6+ -2x^2 +19x=180 first move 180 to other side (don't forget to change its sign

4x^2+ -2x^2 +19x -186=0 combine like terms

2x^2+19x-186=0 know find the greatest common factor

2x(x+19) - 186=0 now we have a degree one equation which will have one answer
2x(x+19)=186 get rid of the 2x by dividing it (invert and multiply)
x+19=186/2x
x+19=93/x get rid of the 1/x by dividing(invert and multiply)
x+19=93*x/1
x+19=93x move the x, don't forget to change its sign
19=92x
x=19/92

Answer 8

First, combine like terms:

4x² - 2x² + 19x - 6 - 180 = 0

2x² + 19x - 186 = 0

Now factor it out (using the quadratic formula):

(2x + 31) * (x - 6) = 0

x = 6 or -15.5