x^2 + 14x - 4 = 0 Solve please?
factor or use quadratic formula i prefer factoring but somethings cant be factor
like this one you cant factor it so use quadratic formula
-b plus or minus the square root of (b^2 -4AC) all of that divided by 2A
A= 1(bc of the 1 in front of the x^2)
b= 14( from the 14x)
C=-4
I would complete the square..
(I use this method when the coefficient of the square term is 1 and the middle term is even)
x^2 + 14x + 49 = 4 + 49
(x+7)^2 = 53
x +7 = ±√53
x = -7 ± √53
oh man i forgot about that method completely lol
It has the advantage over the formula in that it gives you the reduced form of the square root answer right away, while often the answer from the formula has to be simplified.
To solve the given quadratic equation x^2 + 14x - 4 = 0, we can use the quadratic formula. The quadratic formula states that for any quadratic equation in the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
Comparing the given equation to the standard form, we have a = 1, b = 14, and c = -4. Plugging these values into the quadratic formula, we get:
x = (-14 ± √(14^2 - 4(1)(-4))) / (2*1)
Simplifying further, we have:
x = (-14 ± √(196 + 16)) / 2
x = (-14 ± √212) / 2
x = (-14 ± √(4 * 53)) / 2
Now, let's break down the square root of 212. We can factor out the perfect square, 4:
√(4 * 53)
= √4 * √53
= 2 * √53
Substituting this into our equation, we have:
x = (-14 ± 2√53) / 2
We can simplify further by dividing both the numerator and denominator by 2:
x = -7 ± √53
Hence, the solutions to the quadratic equation x^2 + 14x - 4 = 0 are x = -7 + √53 and x = -7 - √53.