Final answer:
To solve the equation -7s² + 7 = 0, divide by -7, find the square root of both sides, giving s = ± 1, and then check that both s = 1 and s = -1 are reasonable solutions by substituting back into the original equation.
Step-by-step explanation:
To solve the quadratic equation -7s² + 7 = 0, we can begin by simplifying the equation and finding values of s that make the equation true. First, isolate s² by dividing both sides of the equation by -7:
-7s² + 7 = 0
-7s² = -7
s² = 1
Next, take the square root of both sides of the equation to solve for s. There are two solutions since the square root of 1 can be positive or negative:
s = ±√1
s = ± 1
The solutions are s = 1 and s = -1. We then need to check the answer to ensure it is reasonable. Plugging both values back into the original equation shows that they do indeed satisfy the equation:
-7(1)² + 7 = 0
-7(-1)² + 7 = 0
So, both s = 1 and s = -1 are valid solutions.