121y^2-196=0
To solve the equation 121y² - 196 = 0, we can use the method of factoring or applying the quadratic formula. Let's start with factoring:
1. Rearrange the equation to have the squared term on one side and the constant term on the other side: 121y² = 196.
2. Divide both sides of the equation by the coefficient of the squared term (121) to isolate y²: y² = 196/121.
3. Take the square root of both sides to eliminate the squared term: y = ±√(196/121).
4. Simplify the square root of 196/121: y = ±14/11.
So the solution to the equation 121y² - 196 = 0 is y = 14/11 or y = -14/11.
Alternatively, if you prefer using the quadratic formula:
1. Identify the coefficients in the equation: a = 121, b = 0, c = -196.
2. Substitute these values into the quadratic formula: y = (-b ± √(b² - 4ac))/(2a).
3. Substitute the values of a, b, and c: y = (0 ± √((0)² - 4(121)(-196)))/(2(121)).
4. Simplify the expression inside the square root: y = (0 ± √(0 + 9604))/(242).
5. Simplify further: y = (0 ± √(9604))/(242) = (0 ± 98)/(242).
Hence, the solutions of the equation 121y² - 196 = 0 are y = 98/242 or y = -98/242, which can be simplified to y = 14/11 or y = -14/11.