Question

if i have the equation x^2 - 7x - 20. some people would believe that this equation would have no solution because it cannot be factored do you agree or disagree? i have no clue

Answer 1

thankyou

Answer 2

Just because an equation cannot be factored does not mean that it doesn't have a solution. If you can't factor it, the next best thing is to use the quadratic formula, given by the formula...

x = (-b ± √((b^2) - 4(a*c)))/2a

Therefore, with the equation: x^2 - 7x - 20, you know that...
a = 1
b = -7
c = -20

Plug them in to the quadratic formula and solve for values of x, if they exist. (If they don't exist, then the equation truly does not have any real solutions.)

x = (7 ± √((49) - 4(-20)))/2
x = (7 ± √((49) + 80))/2
x = (7 ± √(129))/2

Now we come to the turning point, where we solve for x for both the plus and minus sign of the plus/minus (±) expression.

x = (7 + √(129))/2 = 9.17891

x = (7 - √(129))/2 = -2.17891

Indeed, this equation does have real solutions. They may not be pretty, but they are real, and they do exist.