Question

What are the solutions to 3(x-10)2=243?

x=1 and x=19
x=-1 and x=-19
x=343/3 and x=-343/3
x=1 and x=19
x=50.5 and x=30.5

Answer 1

1 and 19

Explanation:

3(x-10)^2 = 3(x^2-20x+100) = 3x^2 - 60x + 300

If 3x^2 - 60x + 300 = 243, 3x^2 - 60x + 57 = 0

Divide by 3 to get x^2 - 20x + 19 = 0

use the quadratic equation (-b±√(b²-4ac))/(2a) to get

(20±√324)/2 = (20±18)/2 = 1 and 19

Answer 2

Simplify the equation by dividing both sides by 3:
(x-10)^2 = 81
Take the square root of both sides of the equation, remembering to include both the positive and negative square roots:
x - 10 = ±9
Solve for x by adding 10 to both sides of the equation:
x = 10 ± 9
Simplify the expression by evaluating both possibilities for x:
x = 10 + 9 or x = 10 - 9
Therefore, the solutions are x=19 and x=1.