I need help can someone help me get unstuck and let me know if i am correct.thank you.
solve by completing the square.
4x^2+2x-3=0
this is what i am doing:
i used the quadratic equation.
so where i am is in this step:
x = (-2 (+-) sqrt (-44))/(8)
from this point i am stuck:
Problem #2
Solve by using the quadratic equation :
5x^2-4x+1=0
this is where i have almost the last step but i am not sure:
x = (4 (+-) sqrt (-4))/(10)
x= (2 +-sqrt )2))/(5)
The first says...complete the square, you did not do that.
4x^2+2x-3=0
4x^2+ 2x = 3
x^2 + 1/2 x = 3/4
Now we add 1/4 to each side
x^2 + 1/2 x + 1/4 = 1
(x+1/2)^2= 1
square root of each side...
x+ 1/2 = +- 1
x= -1/2 +-1
5x^2-4x+1=0
a= 5 b= -4 c= 1
x= (4+-sqrt (16-20) )/10
x= .4 +- 1/10 sqrt-4
x= .4 +- .2i where i is the sqrt-1
To solve the first problem using completing the square:
1. Begin with the equation: 4x^2 + 2x - 3 = 0
2. Move the constant term (-3) to the right side of the equation: 4x^2 + 2x = 3
3. Divide the coefficient of x^2 (4) from both sides of the equation: x^2 + (2/4)x = 3/4
4. Take half of the coefficient of x (2/4) and square it: (2/4)^2 = 1/4
5. Add the result from step 4 to both sides of the equation: x^2 + (2/4)x + 1/4 = 3/4 + 1/4
6. Simplify both sides of the equation: x^2 + (2/4)x + 1/4 = 4/4
7. Rewrite the left side as a perfect square: (x + 1/2)^2 = 4/4
8. Take the square root of both sides: x + 1/2 = ±√(4/4)
9. Simplify the square root: x + 1/2 = ±1
10. Solve for x by subtracting 1/2 from both sides: x = -1/2 ± 1
So, the solutions for the first problem are x = -1/2 + 1 and x = -1/2 - 1.
Moving on to problem 2:
1. Start with the equation: 5x^2 - 4x + 1 = 0
2. Use the quadratic formula: x = (-b ± √(b^2 - 4ac)) / (2a)
a = 5, b = -4, c = 1
3. Plug in the values into the formula: x = (4 ± √((-4)^2 - 4 * 5 * 1)) / (2 * 5)
4. Simplify the expression under the square root: x = (4 ± √(16 - 20)) / (10)
5. Simplify further: x = (4 ± √(-4)) / 10
6. Rewrite the square root of -4 as imaginary number: x = (4 ± 2i) / 10
7. Simplify the expression: x = 0.4 ± 0.2i
So, the solutions for the second problem are x = 0.4 + 0.2i and x = 0.4 - 0.2i.