Question

Solve for

\[x\]. Enter the solutions from least to greatest.
Round to two decimal places.
\[(x + 7)^2 - 11 = 0\]

Answer 1

To solve the equation, take the square root of both sides after isolating the perfect square term and then subtract 7 to find x. The solutions, rounded to two decimal places, are x = -10.32 and x = -3.68.

Step-by-step explanation:

To solve the equation (x + 7)^2 - 11 = 0, we first isolate the perfect square term:

• (x + 7)^2 = 11

Next, we take the square root of both sides of the equation to solve for x:

• √(x + 7)^2 = ±√11
• x + 7 = ±√11

We then isolate x by subtracting 7 from both sides of the equation:

• x = -7 ±√11

Finally, we find the numerical solutions and round them to two decimal places:

• x = -7 + √11 = -3.68
• x = -7 - √11 = -10.32

The solutions are x = -3.68 and x = -10.32, from least to greatest.