Question

Find the solutions to the equation below 4x^2 - 20x + 25 = 10. SHOW STEPS...

a) x = 2 and x = 3
b) x = 5 and x = 7
c) x = 4 and x = 6
d) x = 1 and x = 5

Answer 1

To find the solutions to the equation 4x^2 - 20x + 25 = 10, we rearrange the equation and apply the quadratic formula. The solutions are x = 2 ± √10.

Step-by-step explanation:

The given equation is 4x^2 - 20x + 25 = 10. To find the solutions, we need to rearrange the equation to get it in the form of ax^2 + bx + c = 0. Subtract 10 from both sides to get 4x^2 - 20x + 15 = 0. Now, we can apply the quadratic formula to find the solutions:

x = (-b ± √(b^2 - 4ac)) / (2a)

Plugging in the values for a = 4, b = -20, and c = 15, we get:

x = (-(-20) ± √((-20)^2 - 4(4)(15))) / (2(4))

Simplifying that equation gives us x = (20 ± √(400 - 240)) / 8. And further simplification gives us x = (20 ± √160) / 8. Finally, we can simplify the square root to get x = (20 ± 4√10) / 8. Thus, the solutions to the equation are x = 2 ± √10.