y^2 + 1/4 = -y
how do i do this??? I'm stuck
multiply both sides by 4, gather terms.
4Y^2+4y+1=0
(2y+1)^2=0
y= -1/2
y^2 + y + 1/4 = 0
y = [ -1 +/- sqrt (1 -1) ]/2
= -1/2
double zero at -1/2
To solve the equation y^2 + 1/4 = -y, you can follow these steps:
Step 1: Move all terms to one side of the equation to make it look like a quadratic equation. In this case, add y to both sides:
y^2 + y + 1/4 = 0
Step 2: Multiply both sides of the equation by 4 to eliminate the fraction:
4(y^2 + y + 1/4) = 4(0)
4y^2 + 4y + 1 = 0
Step 3: Now, you can solve this quadratic equation using any suitable method, such as factoring, completing the square, or using the quadratic formula. In this case, let's use the quadratic formula:
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing the quadratic equation 4y^2 + 4y + 1 = 0 with the standard form ax^2 + bx + c = 0, we can determine that: a = 4, b = 4, and c = 1.
Substituting these values into the quadratic formula, we get:
y = (-4 ± √(4^2 - 4 * 4 * 1)) / (2 * 4)
y = (-4 ± √(16 - 16)) / 8
y = (-4 ± √0) / 8
Since the square root of 0 is 0, we have:
y = (-4 ± 0) / 8
This simplifies to:
y = -4 / 8
y = -1/2
Therefore, the solution to the given equation is y = -1/2.