x²-6
What is your question?
Can you help me simplify it?
it's already simple. If you want to factor it, that would be
(x-√6)(x+√6)
It seems like you've entered an expression "x²-6". It appears to be a quadratic equation with the variable "x" squared and a constant term of -6. To solve this equation, we can set it equal to zero and try to find the values of "x" that satisfy the equation.
To solve the equation "x²-6 = 0", we can use the method of factoring, completing the square, or using the quadratic formula. Let's go through each method:
1. Factoring:
The expression "x²-6" cannot be factored further in a simple way since there is no common factor that can be taken out. Therefore, factoring may not be the most straightforward method for this equation.
2. Completing the square:
To complete the square for the quadratic equation "x²-6 = 0", we need to add and subtract a constant term in order to create a perfect square trinomial on the left side of the equation.
To complete the square, we add (6/2)² = 9 to both sides of the equation:
x² - 6 + 9 = 0 + 9
x² + 3 = 9
Now, we can rewrite the left side of the equation as a perfect square trinomial:
(x + √3)² = 9
The equation is now in the form (x + a)² = b, which means that (x + √3)² = 9 can be rewritten as x + √3 = ±√9.
Simplifying that equation, we get two possibilities for the value of "x":
x + √3 = ±3, which gives us two equations:
1. x + √3 = 3
2. x + √3 = -3
Now, we can solve each equation separately to find the value of "x":
1. x + √3 = 3
Subtracting √3 from both sides:
x = 3 - √3
2. x + √3 = -3
Subtracting √3 from both sides:
x = -3 - √3
Therefore, the solutions to the equation "x²-6 = 0" are:
x = 3 - √3
x = -3 - √3
3. Quadratic formula:
The quadratic formula is another method to solve quadratic equations. For the equation "x²-6 = 0", we can use the quadratic formula, which is:
x = (-b ± √(b² - 4ac)) / (2a)
Here, "a" is the coefficient of x², "b" is the coefficient of x, and "c" is the constant term.
Comparing the equation "x²-6 = 0" with the general quadratic equation "ax² + bx + c = 0", we can deduce that:
a = 1, b = 0, c = -6
Substituting these values into the quadratic formula, we get:
x = (-(0) ± √((0)² - 4(1)(-6))) / (2(1))
x = (± √(0 - (-24))) / 2
x = (± √24) / 2
x = ± (√(4 * 6)) / 2
x = ± (√4 * √6) / 2
x = ± (2√6) / 2
x = ± √6
Therefore, the solutions to the equation "x²-6 = 0" are:
x = √6
x = -√6
I hope this explanation helps! Let me know if you have any further questions.