Solve for x X^2+12x+4=0
solving by completing the square, in this case faster than using the formula
x^2 + 12x = -4
x^2 + 12x + 36 = -4 + 36
(x+6)^2 = 32
x+6 = ± √ 32 = ± 4√2
x = -6 ± 4√2
I got -6+4sqrt2,-6-4sqrt2
Is this correct?
Correct.
Isn't that what I wrote ?
I got two solutions.
so did I
-6 ± 4√2 means -6 +4√2 OR -6 -4√2
To solve the quadratic equation x^2 + 12x + 4 = 0, we can use the quadratic formula. The quadratic formula states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, the values of a, b, and c are:
a = 1
b = 12
c = 4
Now we can substitute these values into the quadratic formula:
x = (-(12) ± √((12)^2 - 4(1)(4))) / (2(1))
Simplifying further:
x = (-12 ± √(144 - 16)) / 2
x = (-12 ± √128) / 2
We can simplify the square root of 128 by factoring out the largest perfect square, 16:
x = (-12 ± 4√8) / 2
Now, we can simplify this expression by canceling out the common factor of 4 in the numerator and denominator:
x = -6 ± 2√8
Finally, we can simplify the expression for x:
x = -6 ± 2√(4*2)
x = -6 ± 2√(4)√(2)
Since √(4) = 2, we can simplify further:
x = -6 ± 2(2)√(2)
x = -6 ± 4√(2)
Therefore, the solutions for x in the quadratic equation x^2 + 12x + 4 = 0 are:
x = -6 + 4√(2)
x = -6 - 4√(2)