x^2 - 8x - 126= 0 .không x^4 2528x - 42136
It seems that you are asking about solving or analyzing quadratic and quartic equations in your query. Based on the information you provided, let us address the equations step-by-step:
1. Solve the Quadratic Equation: (x^2 - 8x - 126 = 0)
To solve this quadratic equation (x^2 - 8x - 126 = 0), we will use the quadratic formula:
[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
]
Step 1: Identify the coefficients
For (x^2 - 8x - 126 = 0):
- (a = 1) (coefficient of (x^2)),
- (b = -8) (coefficient of (x)),
- (c = -126) (constant term).
Step 2: Substitute into the formula
Substitute (a), (b), and (c) into the quadratic formula:
[
x = \frac{-(-8) \pm \sqrt{(-8)^2 - 4(1)(-126)}}{2(1)}
]
[
x = \frac{8 \pm \sqrt{64 - 4(1)(-126)}}{2}
]
Step 3: Simplify the discriminant
The discriminant ((b^2 - 4ac)) is:
[
b^2 - 4ac = (-8)^2 - 4(1)(-126) = 64 + 504 = 568
]
So the equation becomes:
[
x = \frac{8 \pm \sqrt{568}}{2}
]
Step 4: Simplify further
(\sqrt{568}) can be simplified:
[
\sqrt{568} = \sqrt{4 \cdot 142} = 2\sqrt{142}
]
Hence, the solution becomes:
[
x = \frac{8 \pm 2\sqrt{142}}{2}
]
[
x = 4 \pm \sqrt{142}
]
Final Answer:
The solutions for (x^2 - 8x - 126 = 0) are:
[
x = 4 + \sqrt{142} \quad \text{and} \quad x = 4 - \sqrt{142}
]
2. Clarify or Rewrite the Quartic Equation
You also mentioned something about a quartic equation written as (x^4 - 2528x - 42136 = 0). Here’s how to approach it:
Step 1: Write the Quartic Equation
The equation appears to be:
[
x^4 - 2528x - 42136 = 0
]
Make sure this equation is written correctly. If not, please revise it.
Step 2: Analyze the Quartic Equation
To solve a quartic equation, numerical or approximation methods may be required. Generally, such equations can also make use of advanced techniques like factorization, synthetic division, or graphing tools, depending on the context. Let me know if you’d like to proceed with further analysis.
If you have a specific question to clarify, feel free to ask! 
I’ll help you step-by-step.