Solve each equation in Exercises 15–34 by the square root propert...

Question

Solve each equation in Exercises 15–34 by the square root property.

2x^2 - 5 = - 55

Accepted Answer

Hello everyone in this video we're going to be looking at this practice problem where we want to solve six K squared plus 63 is equal to nine and we want to try to get a value for K. So in this case We have to try to isolate K on one side of the equation. So I'm going to do that by subtracting 63 and that leaves me with six K squared is equal to negative because negative 63 plus nine is equal to negative 54. So now if I divide by six I have K squared is equal to negative nine. And now you can see I have only K on the left hand side but it's K squared. So in order to just get K I'm going to take the square root of both sides and that leaves me with K is equal to the square root of negative nine. And in order to simplify this further I'm going to separate my square root I'm gonna say K is equal to the square root of negative one Times The Square Root of nine. So now you can see That I can take the square root of nine And the square root is plus or -3 because negative three times negative three is equal to nine and three times three is equal to nine. So I'm left with plus or minus three times the square root of negative one. And here recall that I Imaginary number is equal to the square root of -1. So now wherever I see the square root of negative one I can rewrite it as I so Kay becomes Plus or -3 times I. So that means I have two solutions for K. K could equal three, I Or K could equal negative three high. So that becomes my final answer for K. And you can see that that aligns with answer choice D. So hopefully this video helped and see you next time.

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