4x^2 - 3x + 3 = 0 Solve by completing the square
repeat the procedure I just showed you, tell me what you got.
I divided everything by 4 to get:
x^2 - 3/4x + 3/4 =0
x^2 - 3/4x + 9/64 = -3/4 + 9/64
Here is where I'm stuck
well, you created the perfect square on the left, so state it , and simplify the right side
(x - 3/8)^2 = -39/64
ahhh, I see the problem.
How can anything squared be negative, so there is no REAL number solution.
Have you studied complex numbers?
If so, then
x - 3/8 = ± i√39/8
x = (3 ± i√39)/8
Thanks Reiny - I get stuck on this type of problem every time.
To solve the quadratic equation 4x^2 - 3x + 3 = 0 by completing the square, you'll follow these steps:
Step 1: Divide the entire equation by the leading coefficient (the coefficient of x^2) if it's not 1. In this case, the coefficient is already 4, so we can skip this step.
Step 2: Move the constant term (the term without x) to the right side of the equation. In this case, subtract 3 from both sides:
4x^2 - 3x = -3
Step 3: Take half of the coefficient of x, square it, and add it to both sides of the equation. In this case, the coefficient of x is -3, so:
4x^2 - 3x + (-3/2)^2 = -3 + (-3/2)^2
4x^2 - 3x + 9/4 = -3 + 9/4
Step 4: Simplify the right side of the equation:
4x^2 - 3x + 9/4 = -12/4 + 9/4
4x^2 - 3x + 9/4 = -3/4
Step 5: Rewrite the left side of the equation as a perfect square trinomial. To do this, factor the quadratic expression:
(2x - 3/2)^2 = -3/4
Step 6: Take the square root of both sides of the equation:
2x - 3/2 = ±√(-3/4)
Step 7: Simplify the right side of the equation:
2x - 3/2 = ±(i√3/2), where i is the imaginary unit (√(-1)).
Step 8: Solve for x by isolating it on one side of the equation:
Case 1: 2x - 3/2 = i√3/2
2x = (3 + i√3)/2
x = (3 + i√3)/4
Case 2: 2x - 3/2 = -i√3/2
2x = (3 - i√3)/2
x = (3 - i√3)/4
So, the solutions to the equation 4x^2 - 3x + 3 = 0, obtained by completing the square, are x = (3 + i√3)/4 and x = (3 - i√3)/4.