Question 212975
Solve the given equation by completing the square and applying the square root property


{{{y^2-8y=-7}}}


y=? or y=?


Step 1.  Add 16 to both sides of the equation to get a perfect square on the left.  Why 16?  I divided -8 by 2 which gives -4 and then squared -4 to get 16.


{{{y^2-8y+4^2=-7+4^2}}}


{{{(y-4)^2 = 9}}}


Step 2.  Taking the square root on both sides


{{{sqrt((y-4)^2) = sqrt(9)}}}


{{{y-4= 3}}} and {{{y-4= -3}}}


Solving yields


{{{y-4+4=3+4}}}


{{{y=7}}}  ANSWER


Step 3.  The other solution is found as follows:


{{{y-4= -3}}}


{{{y-4+4 = -3+4}}}


{{{y=1}}} ANSWER


Step 4.  ANSWER IS x=7 and x=1


Step 5.  As a check, the graph of the quadratic equation is shown below and note at x=7 and x=1 intersect the axis when y=0.  So answer is correct


*[invoke quadratic "x", 1, -8, 7 ]


I hope the above steps were helpful.


For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


Good luck in your studies!


Respectfully,
Dr J