x^2-22x=10 solve by completing the square

x^2-22x=10

x^2-22x + 121 = 10 + + 121
(x-11)^2 = 131
x-11 = +-√131
x = +-√131 + 11

To solve the equation x^2 - 22x = 10 by completing the square, follow these steps:

Step 1: Move the constant term to the right side of the equation:
x^2 - 22x + 10 = 0

Step 2: Take half of the coefficient of x and square it. Add this value to both sides of the equation:
x^2 - 22x + (-22/2)^2 = 10 + (-22/2)^2
x^2 - 22x + 121 = 10 + 121

Step 3: Simplify both sides of the equation:
x^2 - 22x + 121 = 131

Step 4: Rewrite the left side of the equation as a perfect square binomial:
(x - 11)^2 = 131

Step 5: Take the square root of both sides to isolate x:
√((x - 11)^2) = √(131)

Step 6: Solve for x:
x - 11 = ±√(131)

Step 7: Add 11 to both sides of the equation to obtain the final solutions:
x = 11 ± √(131)

Therefore, the solutions to the equation x^2 - 22x = 10 are x = 11 + √(131) and x = 11 - √(131).

To solve the quadratic equation x^2 - 22x = 10 by completing the square, follow these steps:

1. Move the constant term to the right side of the equation:
x^2 - 22x - 10 = 0

2. Make sure the coefficient of the x^2 term is 1 by dividing the entire equation by the coefficient:
(1/1) * (x^2 - 22x - 10) = 0
x^2 - 22x - 10 = 0

3. Take half of the coefficient of the x term (-22) and square it:
(-22/2)^2 = (-11)^2 = 121

4. Add the value obtained in step 3 to both sides of the equation:
x^2 - 22x + 121 - 10 = 0 + 121
x^2 - 22x + 111 = 121

5. Write the left side of the equation as a perfect square trinomial by factoring:
(x - 11)^2 = 121

6. Take the square root of both sides of the equation, considering both the positive and negative square roots:
x - 11 = ±√121
x - 11 = ±11

7. Solve for x by adding 11 to both sides of the equation:
x = 11 ± 11

8. Simplify the equation to obtain the two possible solutions for x:
x = 22 or x = 0

Thus, the solutions to the equation x^2 - 22x = 10 are x = 22 or x = 0.