Question

5x^2-25x=125 solve by completeing the square

Answer 1

Answer:

x = 10, -15

Step-by-step explanation:

We can start right away by dividing both sides of our equation by 5 to get the reduced form $x^2-5x=25$.

To "complete the square," or turn the left side of the equation into something we can factor into a perfect square, it helps to remember that for any binomial x - a:

$(x-a)^2=x^2-2ax+a^2$

To "complete" our square, we'll need to add an a² to either side of the equation. To find a, we can set 5x = 2ax and solve:

$5x=2ax\\5/2=a\\25/4=a^2$

Let's add that a² to both sides and simplify!

$x^2-5x+\frac{25}{4}=25+\frac{25}{4}\\\\(x-\frac{5}{2})^2=\frac{125}{4}\\\\x-\frac{5}{2}=\pm\sqrt{\frac{125}{4} } \\\\x=\pm\frac{25}{2}-\frac{5}{2}$

Now we're ready to solve for both value of x:

$x=\frac{25}{2}-\frac{5}{2}=\frac{20}{2} =10\\\\x=-\frac{25}{2}- \frac{5}{2}=-\frac{30}{2} =-15$

So our solutions are x = 10 and x = -15