solve by completing the square x^2-10x=10
x^2 - 10x + 25 = 10 + 25
(x-5)^2 = 35
x-5 = ± √35
x = 5 ± √35
Thank you!
To solve the quadratic equation x^2 - 10x = 10 by completing the square, follow these steps:
Step 1: Move the constant term to the other side of the equation:
x^2 - 10x - 10 = 0
Step 2: To complete the square, take half of the coefficient of the x term, square it, and add it to both sides of the equation:
x^2 - 10x + (-10/2)^2 = 10 + (-10/2)^2
x^2 - 10x + 25 = 10 + 25
Step 3: Simplify both sides of the equation:
x^2 - 10x + 25 = 35
Step 4: Factor the left side of the equation as a perfect square:
(x - 5)^2 = 35
Step 5: Take the square root of both sides of the equation:
√(x - 5)^2 = ±√35
Step 6: Solve for x by adding or subtracting the square root of 35 on both sides:
x - 5 = ±√35
Step 7: Add 5 to both sides of the equation to obtain the final solutions:
x = 5 ± √35
Therefore, the solutions to the equation x^2 - 10x = 10 are x = 5 + √35 and x = 5 - √35.
To solve the equation x^2 - 10x = 10 by completing the square, follow these steps:
Step 1: Move the constant term (10) to the other side of the equation:
x^2 - 10x - 10 = 0
Step 2: Take half of the coefficient of x (-10), square it, and add it to both sides of the equation:
x^2 - 10x + (-10/2)^2 = 10 + (-10/2)^2
x^2 - 10x + 25 = 10 + 25
Step 3: Simplify both sides of the equation:
x^2 - 10x + 25 = 35
Step 4: Rewrite the left side of the equation as a perfect square:
(x - 5)^2 = 35
Step 5: Take the square root of both sides to eliminate the square:
√(x - 5)^2 = ±√35
x - 5 = ±√35
Step 6: Solve for x by adding 5 to both sides of the equation:
x = 5 ± √35
Therefore, the solutions to the equation x^2 - 10x = 10 are x = 5 + √35 and x = 5 - √35.