Copyright

Solve the quadratic equation by completing the square:

{eq}u^2 + 5u + 9 = 0 {/eq}

Question:

Solve the quadratic equation by completing the square:

{eq}u^2 + 5u + 9 = 0 {/eq}

Completing the square method:

Let a quadratic equation be {eq}a{u^2} + bu + c = 0 {/eq}. First make the coefficient of {eq}{u^2} {/eq} unity, that is, {eq}{u^2} + \dfrac{b}{a}u + \dfrac{c}{a} = 0 {/eq}, then shift the constant to right hand side, that is, {eq}{u^2} + \dfrac{b}{a}u = - \dfrac{c}{a} {/eq}. Now, add {eq}{\left( {\dfrac{b}{{2a}}} \right)^2} {/eq} on both sides of equation to get {eq}{u^2} + \dfrac{b}{a}u + {\left( {\dfrac{b}{{2a}}} \right)^2} = {\left( {\dfrac{b}{{2a}}} \right)^2} - \dfrac{c}{a} {/eq}. Then write LHS as the perfect square and solve RHS to obtain {eq}{\left( {u + \dfrac{b}{{2a}}} \right)^2} = \dfrac{{{b^2} - 4ac}}{{4{a^2}}} {/eq} and finally take square root and find the values of {eq}u {/eq}.

Answer and Explanation: 1

Become a Study.com member to unlock this answer!

View this answer

Given

  • The given quadratic equation is {eq}{u^2} + 5u + 9 = 0 {/eq}.

Solution

Re-write the given equation.

{eq}\begin{align*} {u^2} + 5u + 9 &=...

See full answer below.


Learn more about this topic:

Loading...
Completing the Square Practice Problems

from

Chapter 4 / Lesson 8
34K

A quadratic equation in standard form can be turned into one in vertex form by completing the square. Learn the functions of c-values, perfect square binomials, and the standard form of the quadratic equation ins and solve completing-the-square practice problems.


Related to this Question

Explore our homework questions and answers library