Question

Complete the steps in solving the quadratic function 7x – 9 = 7x2 – 49x by completing the square. –9 = 7x2 – x –9 + = 7(x2 – 8x + )

Answer 1

To solve the quadratic function 7x – 9 = 7x² – 49x by completing the square, we can recognize that the left side is a perfect square and simplify the equation to (x - 1)² = 40/7. Solving for x, we find x = 7 + √(40/7) and x = 7 - √(40/7).

Step-by-step explanation:

We can solve the quadratic function 7x – 9 = 7x² – 49x by completing the square. By recognizing that the left side of the equation is a perfect square, we can write it as (x - 1)². Then, by adding 49 to both sides of the equation, we get -9 + 49 = 7(x² - 7x + 49). Simplifying further, 40 = 7(x - 7)².

This is an equation in one variable, so we can solve for x. Dividing both sides by 7, we have (x - 7)² = 40/7. Taking the square root of both sides, we get x - 7 = ±√(40/7). Finally, adding 7 to both sides, we have x = 7 ± √(40/7).

So, the solutions to the quadratic function are x = 7 + √(40/7) and x = 7 - √(40/7).

Answer 2

A) 56 . . . . . . the (negative) sum of -7 and -49

b) 112 . . . . . the product of 7 and 16

c) 16 . . . . . . the square of 8/2