# 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}.

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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 &=...