Question

Solve the equation for all values of x in simplest form: (x + 1)² = 6

Answer 1

To solve the given equation, we take the square root of both sides to find that x equals positive or negative square root of 6 minus 1, which gives us two approximate solutions: 1.45 and -3.45.

Step-by-step explanation:

To solve the equation (x + 1)² = 6 for all values of x, we first take the square root of both sides of the equation to remove the exponent. This gives us two possible solutions because the square root of a number can be both positive and negative. Therefore, we get:

• x + 1 = √6
• x + 1 = -√6

To find the actual values of x, we subtract 1 from both sides:

• x = √6 - 1
• x = -√6 - 1

Those are the solutions in their simplest form. x can be approximately 1.45 or -3.45 when you calculate √6 being roughly 2.45.