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Step by step
- 500.0 v^{2} - 2000.0 = 6000
Start from the equation as given.
- 500.0 v^{2} - 8000.0 = 0
Bring everything to one side and collect like terms so the right-hand side is 0.
- a = 500.0,\quad b = 0.0,\quad c = -8000.0
Read off the coefficients of the standard form ax² + bx + c = 0.
- 8000.0 \left(0.25 v - 1.0\right) \left(0.25 v + 1.0\right) = 0
Factor the quadratic into two linear factors.
- 0.25 v + 1.0 = 0 \;\Rightarrow\; v = -4.0
A product is zero only when one of its factors is zero (zero-product property).
- 0.25 v - 1.0 = 0 \;\Rightarrow\; v = 4.0
A product is zero only when one of its factors is zero (zero-product property).
Reveal the answer
v = -4.0 \quad\text{or}\quad v = 4.0