x^2 - 18x + 81 = 10 + 81
(x-9)^2 = 91
x-9 = ± √91
x = 9 ± √91
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-9)^2 = 91
x-9 = ± √91
x = 9 ± √91
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.