Question

Rewrite the equation in perfect square form
x4² + 2x – 5 =0

Answer 1

The quadratic equation x² + 2x – 5 = 0 is rewritten in perfect square form by completing the square, resulting in the equation (x + 1)² = 6, which can be solved for x.

Step-by-step explanation:

The main answer to the question involves rewriting a quadratic equation in perfect square form. The equation provided appears to have a typo, but if the correct form is x² + 2x – 5 = 0, then to rewrite this in perfect square form, we would complete the square. To describe the explanation step-by-step:

1. Add 5 to both sides to get x² + 2x = 5.
2. Take half of the coefficient of x (which is 2) and square it to get (2/2)² = 1.
3. Add this square to both sides to get x² + 2x + 1 = 5 + 1.
4. The equation x² + 2x + 1 is now a perfect square and can be written as (x + 1)².
5. So the equation becomes (x + 1)² = 6.

Therefore, the equation is now written in perfect square form and can be solved for x by taking the square root of both sides and simplifying further.