Solve the equation for all real solutions in simplest form.4, m, squared, minus, m, minus, 3, equals, minus, m, squared4m 2 −m−3=−m 2
Question
Solve the equation for all real solutions in simplest form.
Solution
To solve the equation 4m^2 - m - 3 = -m^2, we can follow these steps:
Step 1: Combine like terms on both sides of the equation. 4m^2 + m^2 - m + m - 3 = 0
Step 2: Simplify the equation. 5m^2 - 3 = 0
Step 3: Move the constant term to the other side of the equation. 5m^2 = 3
Step 4: Divide both sides of the equation by 5 to isolate m^2. m^2 = 3/5
Step 5: Take the square root of both sides of the equation to solve for m. m = ±√(3/5)
Therefore, the real solutions in simplest form are m = √(3/5) and m = -√(3/5).
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