We can rewrite the equation as ( x + 2 )² = 3
The value of x is -2 ± √3
What is a quadratic equation?
'A quadratic equation is an algebraic equation of the second degree in x. The quadratic equation in its standard form is ax² + bx + c = 0, where a and b are the coefficients, x is the variable, and c is the constant term.'
According to the given problem,
Given equation: x² + 4x + 1 = 0
The equation can be converted to a perfect square by adding 3 on both sides,
⇒ x² + 4x + 1 + 3 = 0 + 3
⇒ x² + 4x + 4 = 3
⇒ ( x + 2 )² = 3
Here, c = 2
d = 3
Now,
Since, this number cannot be factorized,
We apply,
-[tex]\frac{b(+-)\sqrt{b^{2}-4ac } }{2a}[/tex] where, a, b, c are the coefficients of x², x,
= [tex]\frac{-4(+-)\sqrt{4^{2}-4 } }{2}[/tex]
= [tex]\frac{-4(+-)\sqrt{12} }{2}[/tex]
= [tex]-2(+-)\sqrt{3}[/tex]
Hence, we can conclude the value of the equation to be -2 ± √3.
Learn more about quadratic equations here: https://brainly.com/question/2263981
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