Write the equation in standard form for the circle x2+y2+4x=14.

The equation of a circle in standard form is (x-h)² + (y-k)² = r², where (h,k) is the center of the circle and r is the radius.

Given the equation x² + y² + 4x = 14, we can rewrite it in standard form by completing the square for the x terms.

Step 1: Rearrange the equation to group the x terms together: x² + 4x + y² = 14

Step 2: Complete the square for the x terms. To do this, take half of the coefficient of x, square it, and add it to both sides of the equation. Half of 4 is 2, and 2² is 4. x² + 4x + 4 + y² = 14 + 4 (x + 2)² + y² = 18

So, the equation of the circle in standard form is (x + 2)² + y² = 18. This tells us that the center of the circle is at (-2,0) and the radius is the square root of 18, which simplifies to 3√2.