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# Solve the following quadratic equation by completing the square method, ${x^2} + 10x + 24 = 0$.

Last updated date: 27th Mar 2023
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Hint – Add and subtract something to the given equation to make a complete square.

Given equation ,
${x^2} + 10x + 24 = 0$
When we have to solve a quadratic equation in complete square form then we add half of the coefficient of $x$ both sides .
That is we have to add ${\left( {\dfrac{{10}}{2}} \right)^2}$ to both sides of the equation .
So we know,
${\text{ }}{\left( {\dfrac{{10}}{2}} \right)^2} = 25$
${x^2} + 10x + 24 + 25 = 25 \\ {x^2} + 10x + 25 = 25 - 24 \\$
${x^2} + 10x + 25 = {(x + 5)^2} = 1$
$x + 5 = \pm 1 \\ x = - 5 + 1\,\,\,\,\,\& \,\,\,\,\,x = - 5 - 1 \\$
$x = - 6, - 4$
So the value of $x = - 6, - 4$
Note – In these types of problems, we have to know the method of completing square .That is dividing all terms by a(the coefficient of ${x^2}$) . Then add the square of half of the coefficients of $x$ and then solve as above.