The solution for x =
x^2+14x-4=0
x = -14/2 +/- (1/2)sqrt( 196 +16)
= -7 +/- (1/2) sqrt (212)
but 212 = 4*53
so
-7 +/- sqrt(53)
Thank you
To find the solution for x in the equation x^2 + 14x - 4 = 0, you can use the quadratic formula. The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
In this case, the equation is in the form ax^2 + bx + c = 0. Therefore, the values of a, b, and c for our equation are:
a = 1
b = 14
c = -4
Now, substitute these values into the quadratic formula:
x = (-(14) ± √((14)^2 - 4(1)(-4))) / (2(1))
Simplifying further:
x = (-14 ± √(196 + 16)) / 2
x = (-14 ± √(212)) / 2
Now, we need to simplify the square root of 212. We can factor out the square of a whole number from 212:
212 = 4 × 53
Since 53 is a prime number, we cannot simplify it any further. Therefore, the square root of 212 is (√4) × (√53) = 2√53.
Substituting this value back into the equation gives us:
x = (-14 ± 2√53) / 2
Now, we can simplify this:
x = -7 ± √53
So, the solutions for x in the equation x^2 + 14x - 4 = 0 are:
x = -7 + √53
x = -7 - √53