Question

Determine the next step for solving the quadratic

equation by completing the square.
0=-2x²+2x+3
1.-3=-2x² + 2x
2.-3= -2(x²-x)
3.-3+
4.
=-2(x²-x+[
=-2(x-1/-)²
5.7=(x-2)²
The two solutions are

Answer 1

To complete the square for the quadratic equation
`\(0 = -2x^2 + 2x + 3\)`, add and subtract
`\((7)/(2)\)` to form
`\(-3 - 2(x - (1)/(2))^2 = 0\)`. The solutions are
`\(x = (1)/(2) \pm (√(7))/(2)\)`.

To complete the square for the quadratic equation
`\(0 = -2x^2 + 2x + 3\)`, the next step is:

`\[ -3 + (7)/(2) = -2(x - (1)/(2))^2 \]`

This expression is obtained by taking half of the coefficient of x, squaring it, and adding it to both sides of the equation. The solution to the quadratic equation is
`\(x = (1)/(2) \pm (√(7))/(2)\)`.

Completing the square involves transforming a quadratic equation into a perfect square trinomial. In this case, we adjust the equation
`\(0 = -2x^2 + 2x + 3\)` by adding and subtracting
`\((7)/(2)\)` to create a perfect square on one side. This helps in solving for x by factoring it into the form
`\((x - (1)/(2))^2 = (7)/(4)\)`, leading to the solutions
`\(x = (1)/(2) \pm (√(7))/(2)\)`.