Solve by completing the square

x^2-18x=10

Could you please explain this process. I have read through the text over and over and I just do not understand the process.

x^2 - 18x + 81 = 10 + 81

(x-9)^2 = 91
x-9 = ± √91
x = 9 ± √91

Thank for the solution but I still don't understand how the process works.

You need to take the middle term (which is 18), take half of it (9) and square it (81). You then add that number to both sides.

Thank you!

Sure, I'd be happy to explain the process of solving the quadratic equation by completing the square.

To solve the equation x^2 - 18x = 10, we can follow these steps:

Step 1: Move the constant term (in this case, 10) to the right side of the equation, so we have x^2 - 18x = -10.

Step 2: To complete the square, we need to add and subtract a constant term to the left side of the equation. The constant term we will add and subtract is half of the coefficient of x, squared. In this case, the coefficient of x is -18, so half of it is -9, and when squared, we get 81.

So, we have x^2 - 18x + 81 - 81 = -10.

Step 3: Simplify the left side by factoring the trinomial (x - 9)^2.

(x - 9)(x - 9) - 81 = -10.

Step 4: Combine like terms and simplify the equation.

(x - 9)^2 - 81 = -10.

Step 5: Move the constant term (-10) to the right side of the equation.

(x - 9)^2 = -10 + 81.

(x - 9)^2 = 71.

Step 6: Take the square root of both sides of the equation to solve for x.

x - 9 = ± √71.

Step 7: Add 9 to both sides to isolate x.

x = 9 ± √71.

So, the solutions to the equation x^2 - 18x = 10 are x = 9 + √71 and x = 9 - √71.