I need help understanding this equation?

Question

Solve the following equation.


x(4x-19)=5

 

x= ______ , ______

Answer 1

Greetings! 

 

Lets first multiply the x by whats in the parenthesis to see what we get and if it makes the problem look easier to solve! We have

4x²-19x=5

 

Now it looks like if we subtract both sides by 5 we'll get a quadratic in the form of ax²+bx+c=0

 

so lets do that subtraction and figure out what our a, b, and c are.

4x²-19x-5=0

 

so we know that a=4, b=-19, and c=-5

 

Now lets apply the quadratic formula to see what answers we get. Were looking for 

 

 

x=(-b ± √(b² - 4ac)) / 2a

 

Plugging in the values that we know x ends up being 5 and - 1/4

 

Note: Be careful when using the quadratic formula. It can be easy to make an algebraic mistake. Try simplifying it a bit before you put the numbers into a calculator to avoid a mistake (If you're allowed one).

 

Answer 2

Hi Mike,

 

First you need to multiply what's outside the parentheses by what's inside the parentheses. . .

 

4x^2 -19x = 5

 

Now subtract 5 from each side--> 4x^2 - 19x - 5 = 0

 

Now use the quadratic equation where a = 4    b = -19   c = -5

 

x = (19 +/- sq root (361 + 80))/8

 

x = (19 + 21)/8     and x = (19 - 21)/8

 

x = 5   x = -1/4

 

Plug these values of x back into the equation to make sure they work.

 

Have fun.

 

Dan