Help please
select the approcimate values of x that are solutions to f(x)=0 where f(x)=-5x^2+8x+5
I so am lost please show me step by step
time to review the quadratic formula, or follow Damian's excellent advice about online solvers.
Sure, I can help you with that! To find the approximate values of x that are solutions to the equation f(x) = 0, we can use the quadratic formula or factoring.
Let's start by using the quadratic formula, which states that for an equation ax^2 + bx + c = 0, the solutions can be found using the formula x = (-b ± √(b^2 - 4ac)) / (2a).
In this case, our equation is f(x) = -5x^2 + 8x + 5, so a = -5, b = 8, and c = 5. Plugging these values into the quadratic formula, we get:
x = (-8 ± √(8^2 - 4(-5)(5))) / (2(-5))
Simplifying this expression gives us:
x = (-8 ± √(64 + 100)) / (-10)
x = (-8 ± √164) / (-10)
To approximate the values of x, let's calculate them separately.
1. For the positive solution:
x = (-8 + √164) / (-10)
x ≈ (-8 + 12.81) / (-10)
x ≈ 0.281
2. For the negative solution:
x = (-8 - √164) / (-10)
x ≈ (-8 - 12.81) / (-10)
x ≈ 2.881
Therefore, the approximate values of x that are solutions to f(x) = 0 are x ≈ 0.281 and x ≈ 2.881.
I hope this helps! Let me know if you have any further questions.