Solve the quadratic equation by completing the square. Verify your answer graphically. (Enter your answers as a comma-separated list.)

16x2 − 24x − 23 = 0

my answer was:
x =16(x−3/4)^2−32

but online website (where i do my assignments that is posted by my teacher), says it is wrong, i just don't understand why.

16 ( x − 3 / 4 )² − 32 = 0

Divide both sides by 16

( x − 3 / 4 )² − 2 = 0

Add 2 to both sides

( x − 3 / 4 )² − 2 + 2 = 0 + 2

( x − 3 / 4 )² = 2

Take the square root of both sides

x − 3 / 4 = ± √2

Add 3 / 4 to both sides

x − 3 / 4 + 3 / 4 = ± √2 + 3 / 4

x = 3 / 4 ± √2

The solutions are:

x = 3 / 4 - √2 and x = 3 / 4 + √2

You've completed the square correctly, but the left side of your equation should be 0, not x.

0 =16(x−3/4)^2−32.
Also, there's more work to do. Rearrange the equation to isolate x. This will take about 4 steps.

Thanks Bosnian

To solve the quadratic equation 16x^2 - 24x - 23 = 0 by completing the square, follow these steps:

Step 1: Set the equation equal to zero if it is not already: 16x^2 - 24x - 23 = 0.

Step 2: Move the constant term (-23) to the right side of the equation: 16x^2 - 24x = 23.

Step 3: Divide throughout the equation by the coefficient of x^2 (16) to make the coefficient unity (1): (16x^2 - 24x)/16 = 23/16.

Simplifying, we get: x^2 - (3/2)x = 23/16.

Step 4: Take half the coefficient of x (-3/2), square it, and add it to both sides of the equation. This completes the square on the left side: x^2 - (3/2)x + (-3/4)^2 = 23/16 + (-3/4)^2.

Simplifying, we get: x^2 - (3/2)x + 9/16 = 23/16 + 9/16.

Step 5: Simplify the right side: x^2 - (3/2)x + 9/16 = 32/16.

Simplifying further, we get: x^2 - (3/2)x + 9/16 = 2.

Step 6: Factor the perfect square trinomial on the left side, and simplify the right side: (x - 3/4)^2 = 2.

Step 7: Take the square root of both sides to solve for x: sqrt((x - 3/4)^2) = sqrt(2).

Removing the square root, we get: x - 3/4 = ±sqrt(2).

Step 8: Solve for x: Adding 3/4 to both sides gives us: x = 3/4 ± sqrt(2).

So, the solutions for the quadratic equation 16x^2 - 24x - 23 = 0, obtained by completing the square, are: x = 3/4 + sqrt(2), x = 3/4 - sqrt(2).

To verify these solutions graphically, you can plot the equation 16x^2 - 24x - 23 = 0 on a graphing calculator or an online graphing tool. The points where the graph intersects the x-axis will correspond to the solutions of the equation.