Answer:
x1=12, x2 = -2
Step-by-step explanation:
Start with the original equation x^2 - 10x = 24.
To complete the square, we need to add and subtract the square of half the coefficient of x, which is (10/2)^2 = 25
rewrite the equation adding and subtracting 25 to complete the square: x^2 - 10x + 25 - 25 = 24.
Simplify the equation by combining like terms and moving the constant to the other side: (x - 5)^2 - 25 = 24
Add 25 to both sides to isolate the squared term: (x - 5)^2 = 49
Take the square roots of both sides: x - 5 = [tex]\sqrt{49[/tex]
Solve for x by adding 5 to both sides: x = 5 + 7
Find the two solutions for x: x1=5+7+12 and x2 = 5 - 7 = -2