How do you factor xsquared-10x-39=0
you need factors of 39 which differ by 10. I suggest 3 and 13. So,
x^2-10x-39 = (x-13)(x+3)
To factor the quadratic equation xsquared - 10x - 39 = 0, you can use the quadratic formula or the factoring method. Let's go through both methods:
1. Quadratic Formula:
The quadratic formula can be used to directly find the roots of the quadratic equation in the form ax^2 + bx + c = 0. For the given equation xsquared - 10x - 39 = 0, the values of a, b, and c are:
a = 1
b = -10
c = -39
The quadratic formula is given by:
x = (-b ± sqrt(b^2 - 4ac)) / (2a)
Substituting the values of a, b, and c into the formula, we get:
x = (10 ± sqrt((-10)^2 - 4*1*(-39))) / (2*1)
Simplifying further:
x = (10 ± sqrt(100 + 156)) / 2
x = (10 ± sqrt(256)) / 2
x = (10 ± 16) / 2
This gives us two possible solutions:
x = (10 + 16) / 2 = 26 / 2 = 13
x = (10 - 16) / 2 = -6 / 2 = -3
Therefore, the roots of the given equation are x = 13 and x = -3.
2. Factoring Method:
To factor the quadratic equation xsquared - 10x - 39 = 0, we need to find two binomials that multiply together to give this quadratic equation.
First, we look for two numbers that multiply to give -39 and add up to -10 (the coefficient of the middle term). After some trial and error, we find that -13 and +3 satisfy these conditions.
So, we can rewrite the middle term -10x as -13x + 3x:
xsquared - 13x + 3x - 39 = 0
Now, we group the terms with common factors and factor by grouping:
(x(x - 13) + 3(x - 13)) = 0
Now, we can see that (x - 13) is common to both terms, so we factor it out:
(x - 13)(x + 3) = 0
Setting each factor equal to zero and solving for x gives us the roots:
x - 13 = 0 -> x = 13
x + 3 = 0 -> x = -3
So, the roots of the given equation are x = 13 and x = -3.