Complete the Square
Solve each equation
x^2+8x+16=16/9
Show work i want to learn!!!
well first you can simplify by (x+4)^2=16/9
I got that part but I just want to compare my answer.
i got 16/3 and 8/3
As Morgan pointed out, your left side is a perfect square
(x+4)^2 = 16/9
x+4 = ± 4/3
x = 4/3 - 4 = -8/3
or
x = -4/3 - 4 = -16/3
your signs were wrong
Thank You Reiny
To solve the equation x^2 + 8x + 16 = 16/9 using the method of completing the square, follow these steps:
Step 1: Move the constant term to the right side of the equation:
x^2 + 8x + 16 - 16/9 = 0
Step 2: Simplify the right side by finding a common denominator:
x^2 + 8x + (144/9 - 16/9) = 0
x^2 + 8x + 128/9 = 0
Step 3: Divide the coefficient of x by 2, square the result, and add it to both sides of the equation to complete the square. In this case, the coefficient of x is 8, so:
x^2 + 8x + (8/2)^2 = (-128/9) + (8/2)^2
x^2 + 8x + 16 = (-128/9) + 16
Step 4: Simplify the right side:
x^2 + 8x + 16 = (-128/9) + 144/9
x^2 + 8x + 16 = 16/9
Step 5: Write the left side of the equation as a perfect square trinomial. The left side can be factored as (x + 4)^2:
(x + 4)^2 = 16/9
Step 6: Take the square root of both sides of the equation:
x + 4 = ±√(16/9)
Step 7: Simplify the right side:
x + 4 = ±(√16) / (√9)
x + 4 = ±(4/3)
Step 8: Solve for x by subtracting 4 from both sides of the equation:
x = -4 ± (4/3)
Step 9: Simplify the right side:
x = -4 - (4/3) OR x = -4 + (4/3)
Step 10: Further simplify the solutions:
x = -16/3 OR x = 4/3
Therefore, the solutions to the equation x^2 + 8x + 16 = 16/9 are x = -16/3 and x = 4/3.