x^4+2x^2-15=0
To find the solutions to the equation x^4 + 2x^2 - 15 = 0, we can use factoring and the quadratic formula.
Step 1: Factor the equation:
The equation can be written as (x^2 + 5)(x^2 - 3) = 0.
Step 2: Set each factor equal to zero:
x^2 + 5 = 0 or x^2 - 3 = 0.
Step 3: Solve the first factor:
For x^2 + 5 = 0, subtract 5 from both sides to get:
x^2 = -5.
Taking the square root of both sides, we get:
x = ±√(-5).
Step 4: Solve the second factor:
For x^2 - 3 = 0, add 3 to both sides to get:
x^2 = 3.
Taking the square root of both sides, we get:
x = ±√3.
Therefore, the solutions to the equation x^4 + 2x^2 - 15 = 0 are:
x = ±√(-5) and x = ±√3.