Solving the Equation x² + 12x + 5 = 0 by Completing the Square
To solve the quadratic equation x² + 12x + 5 = 0 using the completing the square method, follow these steps:
Step 1: Move the constant to the other side
Start by isolating the x terms. Subtract 5 from both sides:
x² + 12x = -5Step 2: Complete the square
To complete the square for the left side, take half of the coefficient of x (which is 12), square it, and add it to both sides:
Half of 12 is 6, and (6)² = 36.Add 36 to both sides:
x² + 12x + 36 = -5 + 36This simplifies to:
x² + 12x + 36 = 31Step 3: Rewrite the left side as a square
The left side can now be written as a perfect square:
(x + 6)² = 31Step 4: Solve for x
Next, take the square root of both sides. Don’t forget to consider both the positive and negative square roots:
x + 6 = ±√31Step 5: Isolate x
Finally, isolate x by subtracting 6 from both sides:
x = -6 ± √31