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### Section 2.5 : Quadratic Equations - Part I

14. Use the Square Root Property to solve the equation.

${x^2} + 15 = 0$

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Start Solution

There really isn’t too much to this problem. Just recall that we need to get the variable on one side of the equation by itself with a coefficient of one. For this problem that gives,

${x^2} = - 15$ Show Step 2

Now all we need to do is use the Square Root Property to get,

$x = \pm \sqrt { - 15} = \pm \sqrt {15} \,i$

So we have the following two solutions : $\require{bbox} \bbox[2pt,border:1px solid black]{{x = - \sqrt {15} \,i\,\,\,{\mbox{and }}x = \sqrt {15} \,i}}$ .

Do not get excited about complex solutions. They will happen fairly regularly when solving quadratic equations so we need to be able to deal with them.