Answer:
x=4
Explanation:
Given equation: 2x^2 - bx - 20 = 0
We are also given one of the solutions, which is -2.5.
We can start off by substituting -2.5 in place of x, in the given equation.
This is what it will look like:
2 * (2.5) ^2 - b (-2.5) - 20 = 0
After simplifying, the equation will now look like this:
12.5 + 2.5b - 20 = 0
Now, move all of the similar terms to one side of the equation:
2.5b = 20 - 12.5, which is basically 2.5b = 7.5
Divide 2.5 from both sides of the equation:
b = 7.5/2.5, which is b = 3
Now that we know what the value of "b" is, let's go back to the given equation (2x ^2 - bx - 20 = 0), and substitute "3" in place of "b".
It will look like this:
2x^2 - 3x - 20 = 0
We can now apply the Quadratic formula. The formula looks like this:
(-b ± √b^2 -4ac)
2a
Substitute the values from the new equation into the formula:
3 ± √9 + 160
4
Simplify that:
3 ± 13
4
You should now have two solutions:
x1 = 3 + 13, which is x1 = 16/4 = 4
4
x2 = 3 - 13 , which is x2=-10/4, = -2.5
4
Now, the root that was given to us at the start of the problem was -2.5, so the other solution is 4, which we just solved for.
I hope this helps!!