Question

Joyce is trying to solve the equation y = x2 − 8x + 7 using the quadratic formula. She has made an error in one of the steps below. Find the step where Joyce went wrong.

Answer 1

Answer:

x = 1 , 7

Step-by-step explanation:

Solution:-

- The given equation is as follows:

                          y = x^2 - 8x + 7

- We can solve the above equation by either making factors or by using Quadratic formula.

Factor Approach:

- Using the constant "7" at the end of the quadratic equation we will determine two integer multiples such that their additions/subtraction results in "-8".

- So the only factor of "7" are:

                        7 x 1 = 7

                       -7 x -1 = 7

- We see that addition/subtraction of first (7 , 1 ) does not results in "-8", However, the sum of ( -1 , -7 ) = -1 - 7 = -8. So the correct factors are ( -1 , -7 ). So we replace "-8x" with our factors "-1x" and "-7x":

                       x^2 -x -7x + 7 = 0

- Take common multiples out of pair of two terms:

                        x*(x-1) -7*(x-1) = 0

                        (x-7)*(x-1) = 0

- So we equate each term in bracket with "0" and evaluate the values of x:

                        (x-7) = 0  , x = 7

                        (x-1) = 0   , x = 1

- So the solution to the quadratic equation is:

                        x = 1 , 7