We want to solve the equation x² + 16 = 0.
Step 1: Move the constant to the other side of the equation:
x² = -16
Step 2: Take the square root of both sides to solve for x. Since the right side is a negative number, we can break it down into the product of the square root of -1 and the square root of 16:
√x² = √(-1) * √(16)
The square root of -1 is represented by the imaginary unit i, and the square root of 16 is 4:
√x² = i * 4
x = ± 4i
Summary: The solutions to the equation x² + 16 = 0 are two complex numbers: x = 4i and x = -4i. This is achieved by taking the square root of -1 (represented by i) and multiplying it by the square root of 16 (which is 4).
We want to check the solutions to the equation x² + 16 = 0, which are x = 4i and x = -4i.
Step 1: Substitute x = 4i into the original equation:
(4i)² + 16 = 16i² + 16 = -16 + 16 = 0
The left side equals the right side, so x = 4i is a valid solution.
Step 2: Substitute x = -4i into the original equation:
(-4i)² + 16 = 16i² + 16 = -16 + 16 = 0
The left side equals the right side, so x = -4i is also a valid solution.
Summary: By substituting the solutions x = 4i and x = -4i back into the original equation x² + 16 = 0, we have verified that both solutions are correct.
We want to solve the equation x² + a = 0.
Step 1: Move the constant to the other side of the equation:
x² = -a
Step 2: Take the square root of both sides to solve for x. Since the right side is a negative number, we can break it down into the product of the square root of -1 and the square root of a:
√x² = √(-1) * √a
The square root of -1 is represented by the imaginary unit i, and the square root of a is represented by √a:
√x² = i * √a
x = ± i√a
Summary: The solutions to the equation x² + a = 0 are two complex numbers: x = i√a and x = -i√a. This is achieved by taking the square root of -1 (represented by i) and multiplying it by the square root of a.