Solve for the roots in simplest form by completing the square:5, x, squared, plus, 40, x, minus, 410, equals, 05x 2 +40x−410=0

Sure, let's solve the quadratic equation step by step:

1. First, write down the equation: 5x^2 + 40x - 410 = 0

2. Divide the entire equation by 5 to simplify: x^2 + 8x - 82 = 0

3. Now, we need to complete the square. To do this, take the coefficient of x, divide it by 2 and square it: (8/2)^2 = 16

4. Add and subtract this number inside the equation: x^2 + 8x + 16 - 16 - 82 = 0

5. This can be rewritten as: (x + 4)^2 - 98 = 0

6. Now, solve for x by first adding 98 to both sides: (x + 4)^2 = 98

7. Then, take the square root of both sides: x + 4 = ± sqrt(98)

8. Finally, subtract 4 from both sides to solve for x: x = -4 ± sqrt(98)

So, the roots of the equation are x = -4 + sqrt(98) and x = -4 - sqrt(98).