Question

Rewrite the equation by completing the square. g(x)=4x² −16x⁷ .

Answer 1

To rewrite the equation g(x) = 4x² − 16x⁷ by completing the square, we must first address the potential typo in the exponent. Assuming the corrected equation is g(x) = 4x² − 16x, we divide by 4, take half of the coefficient of x (-4), square it, add and subtract it inside the equation, and then factor to get the completed square form g(x) = 4(x - 2)² - 16.

Step-by-step explanation:

To complete the square for the equation g(x) = 4x² − 16x⁷, there seems to be a typo in the exponent of the second term since it is unusual to have such a high exponent in a binomial quadratic expression. Assuming the correct equation is g(x) = 4x² − 16x, we can proceed with the following steps:

1. Divide the equation by the coefficient of x², which is 4, to simplify the completing the square process: g(x)/4 = x² - 4x.
2. Take half of the coefficient of x, which is -4, and square it to find the number to complete the square: (-4/2)² = 4.
3. Add and subtract this number inside the equation: g(x)/4 = x² - 4x + 4 - 4.
4. Write the first three terms as a perfect square and simplify: g(x) = 4(x - 2)² - 16.

The equation is now rewritten by completing the square.