if 2/y+2=-3?y-3,then what is the value of y?
To find the value of y in the equation 2/y + 2 = -3(y - 3), we will solve this equation step by step.
Step 1: Distribute the -3 on the right side of the equation:
2/y + 2 = -3y + 9
Step 2: Multiply the denominators to eliminate fractions:
(2/y) * y + 2y = (-3y + 9) * y
Simplifying:
2 + 2y = -3y^2 + 9y
Step 3: Rearrange the equation to bring all terms to one side:
0 = -3y^2 + 9y - 2y - 9
Step 4: Combine like terms:
0 = -3y^2 + 7y - 9
Step 5: Set the equation equal to zero:
-3y^2 + 7y - 9 = 0
Step 6: Solve the quadratic equation. In this case, we can either factor, complete the square, or use the quadratic formula. Let's use the quadratic formula here.
The quadratic formula is given by:
y = (-b ± √(b^2 - 4ac)) / (2a)
Comparing the equation to the quadratic formula, we have:
a = -3, b = 7, c = -9
Substituting the values into the formula:
y = (-7 ± √(7^2 - 4(-3)(-9))) / (2(-3))
Simplifying:
y = (-7 ± √(49 - 108)) / (-6)
y = (-7 ± √(-59)) / (-6)
Step 7: Since we have a negative value under the square root, the quadratic equation has no real solutions. Therefore, the equation 2/y + 2 = -3(y - 3) has no real solutions for y.