Solve the quadratic equation by completing the square. Verify your answer graphically. (Enter your answers as a comma-separated list.)
16x2 − 24x − 23 = 0
I got this answer:
16(x−3/4)^2−32=0.
Is the answer i got correct?
hello why no answer?
sorry - I was living my life.
Your answer is correct.
To solve the quadratic equation 16x^2 − 24x − 23 = 0 by completing the square, follow these steps:
Step 1: Move the constant term to the other side of the equation:
16x^2 − 24x = 23
Step 2: Divide the equation by the coefficient of x^2 to make the coefficient 1:
x^2 − (24/16)x = 23/16
Step 3: Take half of the coefficient of x, square it, and add it to both sides of the equation:
x^2 − (24/16)x + (24/32)^2 = 23/16 + (24/32)^2
x^2 − (24/16)x + (24/32)^2 = 23/16 + 9/16
x^2 − (24/16)x + (3/4)^2 = 32/16
x^2 − (24/16)x + 9/16 = 2
Step 4: Factor the perfect square trinomial on the left-hand side:
(x - 3/4)^2 = 2
Step 5: Take the square root of both sides of the equation:
x - 3/4 = ±√2
Step 6: Solve for x:
x = 3/4 ± √2
Now let's verify the answer graphically. We will graph the equation 16x^2 − 24x − 23 and find the x-values where it intersects the x-axis.
To graph the equation, plot the points (x, y) that satisfy the equation. You can use a computer or graphing calculator to do this. Alternatively, you can use any graphing software or website.
After graphing the equation, look for the points where the graph intersects the x-axis. The x-coordinates of these points are the solutions to the quadratic equation.
By visually inspecting the graph, you can verify if the values you obtained for x, namely x = 3/4 ± √2, are correct.
Note: If you don't have access to graphing tools, you can use an online graphing calculator or ask for more help to verify the answer.