Question

1) Solve the quadratic equation by completing the square. 6x2 + 4x - 5 = 0

Answer 1

To solve the quadratic equation 6x^2 + 4x - 5 = 0 by completing the square: Divide the entire equation by the coefficient of x^2 to make the coefficient equal to 1. Move the constant term to the right side of the equation. Take half of the coefficient of x, square it, and add it to both sides of the equation. Simplify the equation and write the left side as a perfect square. Set the right side equal to the left side and solve for x.

Step-by-step explanation:

To solve the quadratic equation 6x2 + 4x - 5 = 0 by completing the square:

1. Make sure the equation is in the form ax2 + bx + c = 0
2. Here, a = 6, b = 4, and c = -5.
3. Divide the entire equation by 'a' to make the coefficient of x2 equal to 1.
4. Dividing the equation by 6 gives us x2 + (2/3)x - 5/6 = 0.
5. Move the constant term (-5/6) to the right side of the equation.
6. The equation becomes x2 + (2/3)x = 5/6.
7. Take half of the coefficient of x (2/3) and square it. Add this value to both sides of the equation.
8. The equation becomes x2 + (2/3)x + (2/3)2 = 5/6 + (2/3)2. This simplifies to x2 + (2/3)x + 1/9 = 5/6 + 4/9.
9. Simplify the right side of the equation.
10. The right side becomes 15/18 + 8/18, which simplifies to 23/18.
11. Write the left side of the equation as a perfect square.
12. The left side can be written as (x + 1/3)2.
13. Set the right side of the equation equal to the left side.
14. We have (x + 1/3)2 = 23/18.
15. Take the square root of both sides of the equation.
16. x + 1/3 = ±√(23/18).
17. Isolate x by subtracting 1/3 from both sides of the equation.
18. x = -1/3 ±√(23/18) - 1/3.

Answer 2

You’re answer is x=-7/4 or x=- 1 whole and 3/4 or x=-1.75 whatever u want to choose.