Solve the equation for all values of x by completing the square.

Question

x, squared, plus, 24, equals, 10, x
x
2
+24=
10x

Answer 1

To solve this equation by completing the square, we first need to move all terms to one side of the equation:

x^2 + 24 = 10x

Rearranging the terms:

x^2 - 10x + 24 = 0

Next, we take the coefficient of x (which is -10) and divide it by 2, then square the result:

(-10 / 2)^2 = (-5)^2 = 25

Add and subtract this result inside the parentheses on the left side of the equation:

x^2 - 10x + 25 - 25 + 24 = 0

Simplify:

(x - 5)^2 - 1 = 0

Now, add 1 to both sides of the equation:

(x - 5)^2 = 1

Take the square root of both sides:

x - 5 = ±√1
x - 5 = ±1

Now solve for x:

x = 5 + 1
x = 6

x = 5 - 1
x = 4

Therefore, the solutions to the equation x^2 + 24 = 10x are x = 6 and x = 4.