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Section 2.5 : Quadratic Equations - Part I
14. Use the Square Root Property to solve the equation.
\[{x^2} + 15 = 0\]Show All Steps Hide All Steps
Start SolutionThere 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 2Now 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.