Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. −2y2 + 6y = −2 –3.3, 0.3 –0.3, 3.3 –0.61, 6.61 –11.5, 14.5
To solve the equation -2y^2 + 6y = -2 using the quadratic formula, we need to rewrite the equation in standard form first:
-2y^2 + 6y + 2 = 0
Now we can identify a=-2, b=6, and c=2. The quadratic formula is:
y = (-b ± √(b^2 - 4ac)) / 2a
Substitute in the values:
y = (-6 ± √(6^2 - 4*(-2)*2)) / 2*(-2)
y = (-6 ± √(36 + 16)) / -4
y = (-6 ± √52) / -4
Now we can calculate the two possible solutions:
1. y = (-6 + √52) / -4 ≈ -3.3
2. y = (-6 - √52) / -4 ≈ 0.3
Therefore, the solutions to the equation are y ≈ -3.3 and y ≈ 0.3. So the answer is:
-3.3, 0.3