MATH SOLVE

4 months ago

Q:
# find the solutions to the equation by compelting the square x^2-6x=7

Accepted Solution

A:

Answer:The solution set is {-1, 7}Step-by-step explanation:Rewrite x^2-6x=7 as x^2 - 6x = 7.Identify the coefficient of the x term; it is -6.Halve this coeff (obtaining -3)Square this result (obtaining 9)Add 9 to x^2 - 6x and then subtract 9 from the result: x^2 - 6x + 9 - 9Then we have:x^2 - 6x + 9 - 9 = 7. Add 9 to both sides, obtainingx^2 - 6x + 9 = 16Rewrite x^2 - 6x + 9 as the square of a binomial: (x - 3)^2Then we have (x - 3)^2 = 16Taking the square root of both sides, we getx - 3 = ±4, so that: x = 3 + 4 = 7, and x = 3 - 4 = -1.The solution set is {-1, 7}.