What the solution of the equation: y^2-3y=9 ?
y^2 - 3y - 9 = 0
use the quadratic formula
y^2-3y=9
y^2 - 3y = 9
complete the square
y^2 - 3y + 9/4 = 9 + 9/4
(y - 3/2)^2 = 45/4
+- (y - 3/2) = 45/4
solve for y
y = 3/2 (sqrt5 + 1)
y = -3/2 (-1 + sqrt5)
To find the solution of the equation y^2 - 3y = 9, we'll go through the steps one by one:
Step 1: Write the equation:
y^2 - 3y = 9
Step 2: Rewrite the equation in standard form:
y^2 - 3y - 9 = 0
Step 3: Factorize the quadratic equation, if possible. In this case, the equation cannot be easily factored. So, we move to the next step.
Step 4: Use the quadratic formula to find the solutions:
The quadratic formula is given by:
y = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = -3, and c = -9. Plugging these values into the formula, we get:
y = (-(-3) ± √((-3)^2 - 4(1)(-9))) / (2(1))
y = (3 ± √(9 + 36)) / 2
y = (3 ± √45) / 2
Step 5: Simplify the square root:
√45 = √(9 × 5) = √9 × √5 = 3√5
Step 6: Simplify the solutions:
So, the solutions are:
y = (3 + 3√5) / 2
y = (3 - 3√5) / 2
These are the solutions to the equation y^2 - 3y = 9.