solve y^2-4y=13 using completing the square method
y^2-4y + (-4/2)^2=13+(-4/2)^2
y-4y+4=13+4
(y-2)^2-(sqrt(17))^2=0
(y-2-sqrt17)(y-2+sqrt17)=0
y= 2+sqrt17, y=2-sqrt17
To solve the equation y^2 - 4y = 13 using the completing the square method, follow these steps:
Step 1: Move the constant term to the right side of the equation:
y^2 - 4y - 13 = 0
Step 2: To complete the square, add the square of half the coefficient of the y-term to both sides of the equation. The coefficient of the y-term is -4, so half of it is -2, and the square of -2 is 4:
y^2 - 4y + 4 - 13 = 4
Step 3: Simplify both sides of the equation:
(y - 2)^2 - 13 = 4
Step 4: Move the constant term from the left side of the equation to the right side:
(y - 2)^2 = 17
Step 5: Take the square root of both sides of the equation:
√((y - 2)^2) = ±√17
Step 6: Solve for y:
y - 2 = ±√17 or y - 2 = -√17
Step 7: Add 2 to both sides of the equation:
y = 2 ±√17 or y = 2 - √17
So, the solution to the equation y^2 - 4y = 13 using the completing the square method is y = 2 ±√17 or y = 2 - √17.