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.(4x - 1)^2 = 16

Accepted Answer

Hello. Everyone in this video we're going to be looking at this practice problem where we want to solve for X. In the equation seven x plus one squared is equal to 49. So in this case you can see that the X. Is inside of this exponent. So in order to help us solve for X, you can take the square root of both sides. But when we take the square root of both sides because of the square root property, recall that the square root could be plus or minus The Square Root of 49. And taking the square root on the left hand side cancels out the exponents. So we're left with seven X plus one. So in this case the square root of 49 is equal to seven. So the right hand side is plus or minus seven and the left hand side is seven X plus one. And we still need to solve for X. So I also tracked one from both sides so it leaves me with seven X is equal to plus or minus seven minus one and then I'll divide by seven and finally X is isolated or I have plus or minus seven minus one divided by seven. And this still looks complicated but I can simplify it by realizing that there's two solutions for X I could have a positive seven minus one divided by seven or I could have a negative seven minus one divided by seven. So if the seven is positive I have seven minus one which is six divided by seven and if the seven is negative I have negative seven minus one, which is negative eight divided by seven. So X could either be six divided by seven or negative eight divided by seven. So this becomes my final solutions for X in this equation, and you can see that answer choice C also has positive 6/7 and negative 8/7. So hopefully this video helped and see you next time.

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Solve each equation in Exercises 15–34 by the square root property.(4x - 1)^2 = 16

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