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.