How to solve
x2-2x-13=0
Do you mean:
x^2 - 2x - 13 = 0?
(x^2 = x squared.)
If you have typed your equation correctly, I don't see any solution.
To factor, you would want to find numbers that would give you a product of -13. One would have to be negative and the other positive to give you a negative value. However, 13 is a prime number, so the only choices are 1 and 13. They would not give you -2 for your middle term.
However, if your equation was:
X^2 - 12x - 13 = 0
Then it would factor into:
(x-13)(x+1) = 0
Giving you the answers of x = 13 or -1.
(It helps to type your information correctly.)
x^2x-13=0
i want to solve x2 – 2x – 13 = 0
To solve the quadratic equation x^2 - 2x - 13 = 0, you can use the quadratic formula or factorization.
1. Using the Quadratic Formula:
The quadratic formula is derived from completing the square. For a quadratic equation in the form of ax^2 + bx + c = 0, the quadratic formula is x = (-b ± √(b^2 - 4ac)) / (2a).
In the given equation, a = 1, b = -2, and c = -13. Substituting these values into the formula, we get:
x = (-(-2) ± √((-2)^2 - 4 * 1 * -13)) / (2 * 1)
x = (2 ± √(4 + 52)) / 2
x = (2 ± √56) / 2
x = (2 ± 2√14) / 2
Simplifying further, x = 1 ± √14.
Therefore, the solution to the equation x^2 - 2x - 13 = 0 is x = 1 + √14 or x = 1 - √14.
2. Factoring:
To solve the equation by factoring, we need to find two numbers whose product is equal to -13 and whose sum is equal to -2 (the coefficient of x).
The numbers that satisfy these conditions are -13 and 1. So, we can rewrite the equation as:
(x - 13)(x + 1) = 0
Setting each factor equal to zero, we get:
x - 13 = 0 or x + 1 = 0
Solving these equations gives us:
x = 13 or x = -1
Hence, the solutions to the equation x^2 - 2x - 13 = 0 are x = 13 and x = -1.