Solve the equation for all real solutions in simplest form.2, c, squared, minus, 5, c, minus, 14, equals, minus, 52c 2 −5c−14=−5
Question
Solve the equation for all real solutions in simplest form.2, c, squared, minus, 5, c, minus, 14, equals, minus, 52c 2 −5c−14=−5
Solution
To solve the equation 2c^2 - 5c - 14 = -5, we can follow these steps:
Step 1: Move all terms to one side of the equation to set it equal to zero: 2c^2 - 5c - 14 + 5 = 0
Step 2: Combine like terms: 2c^2 - 5c - 9 = 0
Step 3: Factor the quadratic equation: (2c + 1)(c - 9) = 0
Step 4: Set each factor equal to zero and solve for c: 2c + 1 = 0 or c - 9 = 0
For the first factor: 2c + 1 = 0 2c = -1 c = -1/2
For the second factor: c - 9 = 0 c = 9
Therefore, the real solutions to the equation 2c^2 - 5c - 14 = -5 are c = -1/2 and c = 9.
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