What is the smallest member of the solution set of x^2=30-13x?
x^2 + 13x - 30 = 0
(x-2)(x+15) = 0
x = 2 or x = -15
which is the smaller ?
To find the smallest member of the solution set of the equation x^2 = 30 - 13x, we need to solve for x.
1. Start by moving all terms to one side of the equation to set it to zero:
x^2 + 13x - 30 = 0
2. This equation now needs to be factored, or we can use the quadratic formula to find the solutions.
Factoring method:
The factored form of the quadratic equation is (x - a)(x - b) = 0, where a and b are the roots.
In this case, we need to find two numbers that multiply to -30 (coefficient of the constant term) and add up to +13 (coefficient of the x-term).
By trial and error, we find that the pair of numbers is 15 and -2 (15 * -2 = -30 and 15 + -2 = 13).
So, the factored equation is:
(x + 15)(x - 2) = 0
3. Now, set each factor equal to zero and solve for x:
x + 15 = 0 or x - 2 = 0
Solving these two equations gives us:
x = -15 or x = 2
4. To determine the smallest member of the solution set, we compare the two values of x we found.
Since -15 is less than 2, the smallest member of the solution set of x^2 = 30 - 13x is x = -15.
So, the smallest member of the solution set is x = -15.