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Jobisdone [24]
3 years ago
13

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

Mathematics
1 answer:
IRINA_888 [86]3 years ago
4 0

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 <em>a</em>, 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

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