Solve each equation in Exercises 60–63 by the square root propert...

Question

Solve each equation in Exercises 60–63 by the square root property. x^2/2 + 5 = -3

Accepted Answer

Hello. Today we're going to solve for X. Using the square root property. So the equation given to us is X squared over two minus seven equal to two. Now we want to go ahead and sulfur X. So we need to get X by itself. In order to start that process. What we're going to do is add seven to both sides of this equation. Doing so is going to give me X squared over two equal to seven plus two, which is nine. Now I want to go ahead and get rid of this denominator underneath. X. So in order to do that, I'm gonna go ahead and multiply both sides of the equation by two. Doing so is going to cancel the denominator on the left hand side. Leaving me with just X squared and nine times two is going to be 18 for the right hand side of this equation. So now I need to go ahead and eliminate the exponent from X. Since this is x rays the power of two, I'm gonna go ahead and just take the square root of both sides of this equation. Doing so is just going to leave me with X on the left hand side. But we have the square root of 18 and the square root always produces two values plus or minus. And we're just gonna go ahead and write the square root of 18. Now 18 can be broken down into a product of prime numbers, 18 can be rewritten as nine times two or two is a prime number and nine could be rewritten as three times three, which is a prime number. Putting this back into the square root is going to give me three squared times two. So on the right hand side of this equation, I now have X is equal to plus or minus the square root of three squared times two. Now the square root of three squared is just going to be three and two is a prime number, so I can't take it out of the square root. So what I have now is X is equal to plus or minus three times the square root of two. And that is going to be our solution to this equation. Since we have our solution as X is equal to plus or -3 times the square root of two. The overall solution to this problem is going to be a so I hope this video helps you in understanding the square root property and I'll go ahead and see you all in the next video

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