solve the equation
(x-5)^2=10
(x-5)= +/- √10
x=+/-√10 + 5
your other way of doing is expanding it
(x-5)(x-5)=10
x^2-10x+25=10
bring the 10 over
x^2-10x+15=0
To solve the equation (x-5)^2 = 10, you can follow these steps:
Step 1: Expand the equation
(x-5)^2 = 10
(x-5)(x-5) = 10
Step 2: Simplify the expanded equation
(x^2 - 5x - 5x + 25) = 10
x^2 - 10x + 25 = 10
Step 3: Move all terms to one side of the equation
x^2 - 10x + 25 - 10 = 0
x^2 - 10x + 15 = 0
Step 4: Solve the quadratic equation
To solve a quadratic equation, you can use factoring, completing the square, or the quadratic formula. In this case, the equation can be factored.
(x - 5)(x - 3) = 0
By setting each factor equal to zero:
x - 5 = 0 or x - 3 = 0
Solving for x in each equation:
For x - 5 = 0:
x = 5
For x - 3 = 0:
x = 3
So the solutions to the equation (x-5)^2 = 10 are x = 5 and x = 3.