Final answer:
The equation 5 - 2x² = -5 is solved by adding 5 to both sides, dividing by 2, and taking the square root, resulting in two solutions: x = √5 and x = -√5.
Step-by-step explanation:
Solving a Quadratic Equation Using Inverse Operations
To solve the equation 5 - 2x² = -5 for x using inverse operations, we proceed as follows:
Add 5 to both sides of the equation to get 5 + 5 = 2x².
Simplify to get 10 = 2x².
Divide both sides by 2 to isolate x², yielding x² = 10 / 2.
Simplify further to get x² = 5.
Take the square root of both sides. Remember that there are two solutions to a quadratic equation, thus x = √5 or x = -√5.
To check the solutions, substitute them back into the original equation:
- For x = √5: 5 - 2(√5)² = 5 - 2(5) = 5 - 10 = -5, which confirms the solution.
- For x = -√5: 5 - 2(-√5)² = 5 - 2(5) = 5 - 10 = -5, also confirming the solution.
Both values of x are valid solutions to the equation.