# Solve the quadratic equation.

4x^2-8x+3=5

4x² - 8x +3 - 5 = 0

4x²- 8x - 2 = 0

2x²- 4x -1 = 0

this is as far as I got. I am stuck and do not know what to do next can some one please help?

divide by two:

x²- 2x -1/2 = 0

Now add 1.5 to each side to complete the square:

x²- 2x -1/2 +1.5 = +1.5

(x-1)^{2}=1.5

subtract 1.5 from each side

(x-1)^{2} -1.5 = 0

Now you have a difference of squares (1.5 is sqrt (3/2) squared..)

[x-1-sqrt3/2][x-1+sqrt3/2] = 0

divide by two:

x²- 2x -1/2 = 0

Now add 1.5 to each side to complete the square:

x²- 2x -1/2 +1.5 = +1.5

(x-1)^{2}=1.5

subtract 1.5 from each side

(x-1)^{2} -1.5 = 0

Now you have a difference of squares (1.5 is sqrt (3/2) squared..)

[x-1-sqrt3/2][x-1+sqrt3/2] = 0

the answer is 0

## To solve a quadratic equation, you can use the quadratic formula or factorization. In this case, let's use factorization:

1. Start with the equation: 4x^2 - 8x + 3 = 5.

2. Subtract 5 from both sides: 4x^2 - 8x - 2 = 0.

3. Divide the entire equation by 2 to simplify: 2x^2 - 4x - 1 = 0.

4. Now, we need to find two numbers that multiply to give -1 and add up to give -4, which are -1 and 1.

5. Rewrite the equation using these numbers: (x - 1)(2x + 1) = 0.

6. Set each factor equal to zero: x - 1 = 0 and 2x + 1 = 0.

7. Solve for x: x = 1 and x = -1/2.

So, the solutions to the quadratic equation 4x^2 - 8x + 3 = 5 are x = 1 and x = -1/2.