Final answer:
To solve the quadratic equation 4w^2 + 25 = -20w for w, first rearrange it to standard form and then use the quadratic formula or another method like factoring or completing the square to find the solutions.
Step-by-step explanation:
To solve for w in the quadratic equation 4w2 + 25 = -20w, we need to rearrange the equation into standard form. To do this, we add 20w to both sides of the equation to get 4w2 + 20w + 25 = 0. Now we have a standard quadratic equation and can solve for w by using the quadratic formula, factoring, or completing the square.
The quadratic formula states that for any quadratic equation ax2 + bx + c = 0, the solutions for x can be found with x = (-b ± √(b2 - 4ac)) / (2a). By substituting a = 4, b = 20, and c = 25 into the formula, we can determine the valid solutions for w.