Answer:
Therefore, the constant that needs to be added and subtracted to solve the quadratic equation is 4.
Explanation:
To solve the quadratic equation 9x^2 - 4x - √2 = 0, we can use the method of completing the square. In order to complete the square, we need to determine which constant should be added and subtracted. 1. Look at the quadratic equation: 9x^2 - 4x - √2 = 0. 2. Identify the coefficient of x^2: The coefficient of x^2 is 9. 3. Determine the constant to be added and subtracted: To complete the square, we need to take half of the coefficient of x and square it. In this case, the coefficient of x is -4. Half of -4 is -2, and (-2)^2 is 4. Therefore, the constant to be added and subtracted is 4. 4. Rewrite the equation with the constant added and subtracted: 9x^2 - 4x - √2 + 4 - 4 = 0. 5. Simplify the equation: 9x^2 - 4x + 4 - √2 - 4 = 0. 6. Group the terms: (9x^2 - 4x + 4) - (√2 - 4) = 0. 7. Complete the square for the terms inside the parentheses: (3x - 2)^2 - (√2 - 4) = 0. Now, the quadratic equation is in the form (a - b)^2 - c = 0, where a = 3x - 2, b = √2, and c = √2 - 4.