Exercises 103–105 will help you prepare for the material covered ...

Question

Exercises 103–105 will help you prepare for the material covered in the next section. Solve by completing the square: y² – 6y — 4 = 0.

Accepted Answer

hey everyone here we are asked to complete the square to solve the given equation of y squared minus eight, Y minus three is equal to zero. Now we want to start by getting the y terms alone. So we'll just transpose this negative three to the right side of the equation which gives us y squared minus eight, Y is equal to three. And now from here we can start completing the square so we'll take this coefficient here of why. And we want to divide it by two and then take the square of that quantity. So we have negative eight divided by two, which is negative four. And taking the square of this quantity gives us 16. So to finish completing the square, we'll add the 16 to the left side of the equation. This gives us y squared minus eight, Y plus 16 is equal to three. But since we did something to the left side of the equation, we also have to do it to the right side. So we need to add this 16 to the three here and now we can rewrite the trine Amiel as a square of a binomial. So we can use this negative four here to rewrite the left side of the equation as the quantity of why minus four squared is equal to three plus 16 which is 19. And from here we can just start solving for y. So we first need to get rid of this square so we need to take the square root of both sides. So we have the square root of the quantity of y minus four squared is equal to the square root of 19. And since we added this square root to the 19, we also have to add this plus or minus sign in front of it because if we take the square of The Square Root of 19, This gives us 19, but the negative square root of 19 squared is also equal to 19. So adding this plus or minus here accommodates for both scenarios. So now from here after taking the square root we have Y -4 is equal to plus or minus the square root of 19. And now to get why alone we can just transpose this negative four to the right side of the equation. And this gives us a final answer of why is equal to four plus or minus the square root of 19, which is our answer here for choice. D Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Exercises 103–105 will help you prepare for the material covered in the next section. Solve by completing the square: y² – 6y — 4 = 0.

Key Concepts

Completing the Square

Quadratic Equations

Discriminant

Watch next