Solve the quadratic equation by completing the square x^2-10x-8=0
We'll start off by moving the constant term to the right side of the equation.
x^2 - 10x = 8
From here, we want to find a value that we can add to both sides of the equation to complete the square on the left side. This value is calculated by taking half of the coefficient of the x term (which is -10), squaring it, and then adding it to both sides.
(-10/2)^2 = 25
x^2 - 10x + 25 = 8 + 25
Now, we can simplify the equation.
(x - 5)^2 = 33
Taking the square root of both sides gives us two possible solutions (remember that the square root of a number is both the positive and negative root).
x - 5 = sqrt(33)
x = 5 + sqrt(33)
AND
x - 5 = - sqrt(33)
x = 5 - sqrt(33)
So, the solutions to the quadratic equation x^2 - 10x - 8 = 0 are x = 5 + sqrt(33) and x = 5 - sqrt(33).
Step 1: Move the constant term to the other side of the equation:
x^2 - 10x = 8
Step 2: Take half of the coefficient of x, square it, and add it to both sides of the equation. In this case, the coefficient of x is -10, so (-10/2)^2 = 25, and we add it to both sides:
x^2 - 10x + 25 = 8 + 25
Simplifying the equation gives:
x^2 - 10x + 25 = 33
Step 3: Factor the left side of the equation as a perfect square. Since the square root of x^2 is x, and the square root of 25 is 5, the left side of the equation can be factored as (x - 5)^2:
(x - 5)^2 = 33
Step 4: Take the square root of both sides of the equation:
√((x - 5)^2) = √(33)
Simplifying gives:
x - 5 = ±√(33)
Step 5: Solve for x by adding 5 to both sides of the equation:
x = 5 ± √(33)
Therefore, the solutions to the quadratic equation x^2 - 10x - 8 = 0 are:
x = 5 + √(33) and x = 5 - √(33)
To solve the quadratic equation x^2 - 10x - 8 = 0 by completing the square, follow these steps:
Step 1: Move the constant term to the other side of the equation:
x^2 - 10x = 8
Step 2: Take half of the coefficient of x (-10/2 = -5), square it (-5^2 = 25), and add it to both sides of the equation:
x^2 - 10x + 25 = 8 + 25
This step ensures that the left side of the equation becomes a perfect square trinomial, as we can rewrite it as (x - 5)^2.
Step 3: Simplify the right side of the equation:
x^2 - 10x + 25 = 33
Step 4: Take the square root of both sides of the equation:
√(x^2 - 10x + 25) = ±√33
Simplifying, we have:
(x - 5) = ±√33
Step 5: Solve for x by isolating it on one side of the equation:
x = 5 ± √33
So the solution to the quadratic equation x^2 - 10x - 8 = 0, obtained by completing the square method, is x = 5 + √33 and x = 5 - √33.