77.3k views
4 votes
Solve for u. u^(2)+10u+25=0 If there is more than one solution, If there is no solution, click on "No

1 Answer

3 votes

Sure, let's solve the given equation, u^2 + 10u + 25 = 0. This is a quadratic equation and it is in the standard form: au^2 + bu + c = 0. In this case, a is 1, b is 10, and c is 25.

A quadratic equation can have a maximum of two solutions (real or complex). The solutions for this equation can be found by using the quadratic formula u = [-b ± sqrt(b^2 - 4ac)] / 2a.

Let's calculate the discriminant first, which is the term inside the square root in the quadratic formula. The discriminant is given by: b^2 - 4ac.

Substituting a = 1, b = 10, c = 25, we get discriminant = (10)^2 - 4* 1 * 25 = 100 - 100 = 0.

When the discriminant equals zero, it means the quadratic equation has exactly "one distinct" real solution. This distinct real solution is u = [ -10 ± sqrt(0) ] / 2*1 = -5.

Therefore, the given equation, u^2 + 10u + 25 = 0, has exactly one real solution and it is -5.

User Komputist
by
8.1k points

Related questions

asked Jan 3, 2024 138k views
Alcolawl asked Jan 3, 2024
by Alcolawl
7.9k points
1 answer
0 votes
138k views
asked Jul 6, 2024 153k views
Acer asked Jul 6, 2024
by Acer
8.1k points
1 answer
3 votes
153k views