can someone tell me if i did the problem correct (solve by completing the square) 4x^2+2x-3=0
x^2+(1/2)=3/4
x^2+(1/2)+(1/4)^2=3/4+(1/4)^2
(x+1/4)^2=13/16
x+1/4=+-sqrt 13/16
x+1/4=+-sqrt 13/4
x=-1/4+-sqrt 13/4
x=-1+-sqrt 13/4
x^2+(1/2)=3/4 should say
x^2+(1/2x)=3/4 also in the line that follows that you left out the x in the second term
to avoid problems with order of operation, write your final answer this way
x=(-1+-sqrt 13)/4 the way you have it only the square root term would be divided by 4
To verify if you have correctly solved the quadratic equation by completing the square, we can start from the original equation:
4x^2 + 2x - 3 = 0
1. Divide the entire equation by 4, to simplify the equation:
x^2 + (1/2)x - 3/4 = 0
2. Move the constant term (-3/4) to the other side of the equation:
x^2 + (1/2)x = 3/4
3. In order to complete the square, we need to take half of the coefficient of x (1/2 in this case) and square it:
The square of (1/2) is (1/2)^2 = 1/4.
4. Add this value to both sides of the equation:
x^2 + (1/2)x + 1/4 = 3/4 + 1/4
5. Simplify:
x^2 + (1/2)x + 1/4 = 4/4
x^2 + (1/2)x + 1/4 = 1
6. Factor the left side of the equation:
(x + 1/4)^2 = 1
7. Take the square root of both sides:
sqrt((x + 1/4)^2) = sqrt(1)
8. Simplify:
|x + 1/4| = 1
9. Remove the absolute value by considering both positive and negative possibilities separately:
x + 1/4 = 1 or x + 1/4 = -1
10. Solve for x in each equation:
x = 1 - 1/4 or x = -1 - 1/4
11. Simplify:
x = 3/4 or x = -5/4
Therefore, the correct solutions to the quadratic equation 4x^2 + 2x - 3 = 0, when solved by completing the square, are:
x = 3/4 or x = -5/4
It appears that the answer you provided (-1 ± √13/4) is incorrect.