Question

Determine the next step for solving the quadratic equation by completing the square. 0 = –2x2 + 2x + 3 –3 = –2x2 + 2x –3 = –2(x2 – x) –3 + = –2(x2 – x + ) = –2(x – )2 = (x – )2 The two solutions are

Answer 1

To solve the quadratic equation by completing the square, isolate the x terms by moving the constant term to the other side. Make the left side a perfect square by adding a term equal to half the coefficient of x squared. Factor the left side as a perfect square and take the square root of both sides to solve for x.

Step-by-step explanation:

To solve the quadratic equation by completing the square, the next step is to isolate the x terms by moving the constant term to the other side of the equation. In this case, rewrite the equation as:

x²+0.0211x = 0.0211

Now, we want to make the left side of the equation a perfect square. To do this, we take half of the coefficient of x (0.0211/2 = 0.01055), square it, and add it to both sides of the equation:

x²+0.0211x + (0.01055)² = 0.0211 + (0.01055)²

Simplifying further:

x²+0.0211x + 0.0001109 = 0.0212381

The next step is to factor the left side of the equation as a perfect square:

(x + 0.01055)² = 0.0212381

Finally, take the square root of both sides and solve for x, considering both positive and negative roots:

x + 0.01055 = ±√(0.0212381)

x = -0.01055 ± √(0.0212381)

Therefore, the two solutions are:

x = -0.01055 + √(0.0212381) and x = -0.01055 - √(0.0212381)

Answer 2

-1/2, 1/4, 1/2

Step-by-step explanation: