Solve: x^2 +4x+1=0
Is the answer 2+-sqrt2?
no,
x^2 + 4x = -1
x^2 + 4x + 4 = -1 + 4
(x+2)^2 = 3
x+2 = ±√3
x = -2 ±√3
or use the formula, then simplify
Thanks I understand now.
To solve the quadratic equation x^2 + 4x + 1 = 0, we can use the quadratic formula. The quadratic formula states that for any equation in the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In our case, a = 1, b = 4, and c = 1. Plugging these values into the quadratic formula, we get:
x = (-4 ± √(4^2 - 4(1)(1))) / (2(1))
Simplifying further:
x = (-4 ± √(16 - 4)) / 2
x = (-4 ± √12) / 2
Now, we need to simplify the square root of 12. Since there are no perfect square factors of 12, we can write √12 as √(4 * 3). This can be further simplified as 2√3.
Therefore, the solutions for x are:
x = (-4 + 2√3) / 2 and x = (-4 - 2√3) / 2
Simplifying further:
x = -2 + √3 and x = -2 - √3
Hence, the solutions to the equation x^2 + 4x + 1 = 0 are x = -2 + √3 and x = -2 - √3.