Solve 2x^2-12+4=0 by completing the square, expressing the result in simplest radical form.
I will asssume you have a typo and meant
2x^2-12x+4=0
divide each term by 2
x^2 - 6x = -2
add 9 to both sides
x^2 - 6x + 9 = -2 + 9
(x-3)^2 = 7
take √ root of both sides
x - 3 = ± √7
x = 3 ± √7
yes, thank you for the help
Oh, dear! Completing the square sounds like a tricky task. But don't worry, I'll do my best to help you out while sprinkling a bit of humor along the way!
First, let's start by moving our constant term to the other side and grouping our x terms together. Our equation is now 2x^2 + 4 = 12.
Next, we divide everything by the coefficient of x^2, which is 2. So we have x^2 + 2 = 6.
To complete the square, we take half of the coefficient of x and square it. Half of 2 is 1, and 1 squared is 1.
Now, we add 1 to both sides of the equation, giving us x^2 + 2x + 1 = 7.
Hurray! We turned our equation into a perfect square!
But what's the radical solution, you ask? Well, we can express it as (x + 1)^2 = 7.
To fully unravel the mystery of x, we take the square root of both sides:
x + 1 = ±√7.
And finally, we can isolate x by subtracting 1 from both sides:
x = -1 ± √7.
Voilà! We completed the square and expressed the result in the simplest radical form. Remember, math can be fun with a little clowning around!
To solve the given equation 2x^2 - 12x + 4 = 0 by completing the square, follow these steps:
Step 1: Move the constant term to the right side of the equation:
2x^2 - 12x = -4
Step 2: Divide the entire equation by the coefficient of the x^2 term to make it equal to 1:
x^2 - 6x = -2
Step 3: Take half of the coefficient of the x term (-6), square it (6^2 = 36), and add it to both sides of the equation:
x^2 - 6x + 36 = -2 + 36
x^2 - 6x + 36 = 34
Step 4: Rewrite the left side of the equation as a binomial squared:
(x - 3)^2 = 34
Step 5: Take the square root of both sides of the equation:
√((x - 3)^2) = ± √34
Step 6: Solve for x by isolating it on one side of the equation:
x - 3 = ± √34
Step 7: Add 3 to both sides to get the final solutions for x:
x = 3 ± √34
Hence, the solutions to the equation 2x^2 - 12x + 4 = 0 in simplest radical form are x = 3 + √34 and x = 3 - √34.