Final answer:
To rewrite the equation 0=8x² + 24x − 16 in the form (x-p)² = q, divide the equation by the coefficient of x², complete the square, and rearrange the equation.
Step-by-step explanation:
To rewrite the equation 0=8x² + 24x − 16 in the form (x-p)² = q, we need to complete the square. First, divide the entire equation by the coefficient of x² to make the leading coefficient 1: 0 = x² + 3x - 2. Now, add the square of half the coefficient of x to both sides: 0 + (3/2)² = x² + 3x + (3/2)² - 2. Simplifying further gives: 9/4 = (x + 3/2)² - 2. Rearranging the equation, we have: (x + 3/2)² = 9/4 + 2. Combining the fractions on the right-hand side gives: (x + 3/2)² = 17/4. Therefore, the equation is now in the form (x-p)² = q, where p = -3/2 and q = 17/4.
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