Complete the square to solve the following quadratic equation: x² + 4x = 41.
• X = -2 + 5√3, -2 - 5√3
• X = -2 + 5√3, 2 - 5√3
• X = 2 + 3√5, 2 - 3√5
• X = -2 + 3√5, -2 - 3√5
To complete the square for the quadratic equation x² + 4x = 41, we need to add and subtract a constant on the right side of the equation:
x² + 4x + (4/2)² = 41 + (4/2)²
x² + 4x + 4 = 41 + 4
x² + 4x + 4 = 45
Now, we can write the left side as a perfect square:
(x + 2)² = 45
Taking the square root of both sides:
x + 2 = ±√45
x + 2 = ±√(9 * 5)
x + 2 = ±√9 * √5
x + 2 = ±3√5
Finally, subtracting 2 from both sides:
x = -2 ± 3√5
So, the correct solution to the quadratic equation x² + 4x = 41 is x = -2 ± 3√5. Therefore, the option that matches this solution is:
X = -2 + 3√5, -2 - 3√5.