One of the steps needed to solve a quadratic equation by grouping is to split the middle term as a sum of two terms. Given the equation x2−13x+42=0 , which two numbers would be needed to complete this step? Enter the lesser value first.(1 point)
x2−13x+42=0
x2+
x+
x+42=0
To solve the given quadratic equation x^2−13x+42=0 using grouping, we need to split the middle term, -13x, as a sum of two terms.
To find the two numbers needed, we need to find two numbers whose product is equal to the product of the coefficient of x^2 (which is 1) and the constant term (which is 42) and whose sum is equal to the coefficient of x (which is -13).
The two numbers, in this case, are -6 and -7.
Their sum is -6 + (-7) = -13
Their product is (-6)(-7) = 42
Therefore, the two terms needed to split the middle term are x - 6 and x - 7.