x^2 + x - 72
(x)(x)=x=72
8x8+8=72
(x)(x)=x=72
8x8+8=72
64+8=72
The original problem is not an equation. It has no equal sign.
To find the factors of the given quadratic expression x^2 + x - 72, we can use factoring or the quadratic formula.
1. Factoring:
To factorize the quadratic expression, we need to find two numbers that multiply to give -72 and add up to +1 (the coefficient of x). By trial and error, we can find that the numbers are 9 and -8.
So, we can express the quadratic expression as:
(x + 9)(x - 8)
2. Quadratic Formula:
Alternatively, we can use the quadratic formula to find the roots of the quadratic expression. The quadratic formula states that for any quadratic equation in the form ax^2 + bx + c = 0, the roots can be found using the formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the given quadratic expression x^2 + x - 72, a = 1, b = 1, and c = -72. Plugging in these values into the quadratic formula, we get:
x = (-1 ± √(1^2 - 4(1)(-72))) / (2(1))
x = (-1 ± √(1 + 288)) / 2
x = (-1 ± √289) / 2
x = (-1 ± 17) / 2
So, the two possible roots are:
x = (-1 + 17) / 2 = 8
x = (-1 - 17) / 2 = -9
Therefore, the factors of the quadratic expression x^2 + x - 72 are (x + 9) and (x - 8), and the roots are 8 and -9.