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Sagot :
The solution of the equation is x=3 or x=-5.
Given that the equation is (x+2)²-2(x-+2)-15=0 and use u substitution method to solve.
Let's assume that the (x+2)=u.
The given equation is rewritten as u²-2u-15=0.
Factorize the quadratic equation by adding or subtracting two number that gives the sum of -2u and product 15u² as
u²-5u+3u-15=0
u(u-5)+3(u-5)=0
Taking out (u-5) as common and get
(u-5)(u+3)=0
Compare each equation with 0 and get
u-5=0 or u+3=0
u=5 or u=-3
Performing back substitution by substituting the values of u in x+2
when u=5 then x is
x+2=5
x=3
And when u=-3 then x is
x+2=-3
x=-5
Hence, the solutions of the (x+2)²-2(x-+2)-15=0 is x=3 and x=-5.
Learn about the substitution here brainly.com/question/12802700
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