it relatively is undefined with the aid of fact 2^x is often valuable yet -8 is detrimental. (4(2^x)-a million)((2^x)+8)=0 With this problem, there is just one answer it relatively is x = -2. the factor (2^x + 8) is often valuable for all x's. One factor equals to 0 is sufficient to validate the equation.
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Verified answer
√(10–x) +x = 8
√(10–x) = 8 - x
10–x = 64 - 16x + x^2
x^2 - 15x + 54 = 0
(x - 6)(x - 9) = 0
x = 6
x = 9 ---> reject
x = 6 ----> Answer
If we subtract x from both sides, we get:
√(10 - x) = 8 - x.
Upon squaring both sides:
10 - x = (8 - x)^2
==> 10 - x = x^2 - 16x + 64
==> x^2 - 15x + 54 = 0
==> (x - 9)(x - 6) = 0
==> x = 6 and 9.
Since we have squared both sides, we need to check for extraneous solutions.
i) x = 6 ==> √(10 - 6) + 6 = 8 ==> 8 = 8 (Works)
ii) x = 9 ==> √(10 - 9) + 9 = 9 ==> 10 ≠ 8 (Discard).
Therefore, the solution to the equation is x = 6.
I hope this helps!
Subtract both sides by x.
√(10 - x) = 8 - x
Place ² by both sides, which gives:
10 - x = (8 - x)²
10 - x = 64 - 16x + x²
Bring 10 - x to the right.
0 = 54 - 15x + x²
Factor out the polynomial.
0 = (9 - x)(6 - x)
Set each by zero and solve for x.
9 - x = 0 and 6 - x = 0
Therefore, you have:
x = {9, 6}
I hope this helps!
x = 6
@ other guy: If x = 9 then 10 = 8
it relatively is undefined with the aid of fact 2^x is often valuable yet -8 is detrimental. (4(2^x)-a million)((2^x)+8)=0 With this problem, there is just one answer it relatively is x = -2. the factor (2^x + 8) is often valuable for all x's. One factor equals to 0 is sufficient to validate the equation.
10-x=64+x^2-16x
x^2-15x+54=0
x's=[15+&-(225-216)^1/2]/2=9 & 6
x=9 Not acceptable
x=6 Is acceptable
God bless you.