Using completing the square method solve for x in the following
X+2x+8=0
To solve this equation using the completing the square method, we rearrange the equation so that the constant term is isolated on one side:
x + 2x + 8 = 0
Combine like terms: 3x + 8 = 0
Subtract 8 from both sides: 3x = -8
Next, we divide both sides by the coefficient of x, which is 3:
3x/3 = -8/3
x = -8/3
Therefore, the solution to the equation x + 2x + 8 = 0 using the completing the square method is x = -8/3.
To solve the equation x + 2x + 8 = 0 using the completing the square method, follow these steps:
Step 1: Group the x terms together:
x(x + 2) + 8 = 0
Step 2: Divide the coefficient of the x term by 2 and square it. Add this resulting value to both sides of the equation:
x(x + 2) + 8 + 1 = 1
Step 3: Rewrite the left side of the equation as a perfect square trinomial:
(x + 1)^2 + 7 = 1
Step 4: Subtract 7 from both sides of the equation:
(x + 1)^2 = -6
Step 5: Take the square root of both sides:
√((x + 1)^2) = ±√(-6)
Step 6: Simplify and solve for x:
x + 1 = ±i√6
Subtract 1 from both sides:
x = -1 ± i√6
So the solutions to the equation x + 2x + 8 = 0 using the completing the square method are x = -1 + i√6 and x = -1 - i√6.
To solve the equation using completing the square method, follow these steps:
Step 1: Rearrange the equation
Rearrange the equation to have all the variables on one side and the constant term on the other side:
x + 2x + 8 = 0
Combine the like terms:
3x + 8 = 0
Step 2: Isolate the variable terms
Isolate the variable terms by subtracting the constant term from both sides of the equation:
3x = -8
Step 3: Square the coefficient of the variable term
To complete the square, square half of the coefficient of the variable term and add it to both sides of the equation:
3x + 0 = -8 + (1/2 * 2)^2
3x = -8 + 1
3x = -7
Step 4: Solve for x
Divide both sides of the equation by the coefficient of the variable term to solve for x:
x = -7/3
Therefore, the solution to the equation x + 2x + 8 = 0 using the completing the square method is x = -7/3.