Complete the square to solve the following quadratic equation:
X^2 + 2x – 8 = 0
To complete the square, we need to rewrite the equation in the form (x + a)^2 = b.
First, we move the constant term to the other side of the equation:
x^2 + 2x = 8
Next, we divide the coefficient of x by 2 and square it. Then, we add this value to both sides of the equation:
x^2 + 2x + 1 = 8 + 1
(x + 1)^2 = 9
Now, we take the square root of both sides:
√[(x + 1)^2] = ±√9
x + 1 = ±3
To solve for x, we subtract 1 from both sides:
x = -1 ± 3
This gives us two solutions: x = -4 and x = 2.
To complete the square to solve the quadratic equation, follow these steps:
Step 1: Move the constant term to the other side of the equation:
X^2 + 2x = 8
Step 2: Divide the coefficient of x by 2, then square it:
The coefficient of x is 2, so divide by 2 to get 1.
1^2 = 1
Step 3: Add the squared value to both sides of the equation:
X^2 + 2x + 1 = 8 + 1
(X + 1)^2 = 9
Step 4: Take the square root of both sides of the equation:
√((X + 1)^2) = ±√9
X + 1 = ±3
Step 5: Solve for x by subtracting 1 from both sides of the equation:
X = -1 ± 3
So, the solutions to the quadratic equation X^2 + 2x - 8 = 0 are:
X = -4 or X = 2.
To complete the square, we need to rearrange the equation so that it is in the form of (x + p)^2 = q, where p and q are constants.
To complete the square, we will follow these steps:
Step 1: Move the constant term to the other side of the equation:
X^2 + 2x = 8
Step 2: Add the square of half the coefficient of x to both sides of the equation:
X^2 + 2x + (2/2)^2 = 8 + (2/2)^2
X^2 + 2x + 1 = 8 + 1
Step 3: Simplify both sides of the equation:
X^2 + 2x + 1 = 9
Step 4: Factor the left side of the equation:
(X + 1)(X + 1) = 9
Step 5: Take the square root of both sides of the equation:
√((X + 1)(X + 1)) = ±√9
Step 6: Simplify both sides of the equation:
X + 1 = ±3
Step 7: Solve for X:
X = -1 ±3
So, the solutions to the quadratic equation X^2 + 2x – 8 = 0 after completing the square are X = -4 and X = 2.