The given equation involves a power of the variable. Find all real solutions of the equation. (x-1)^{3}+8=0

smileycellist2

smileycellist2

Answered question

2021-05-01

The given equation involves a power of the variable. Find all real solutions of the equation.
(x1)3+8=0

Answer & Explanation

Ezra Herbert

Ezra Herbert

Skilled2021-05-02Added 99 answers

Step 1
The equation is a statement that consists of equal symbol between two algebraic expressions. The solution for the variable of the equation must satisfy the equation when we resubstitute the solution in the equation.
Step 2
The given equation is (x1)3+8=0. The real solutions of the given equation means the real values for the variable x that satisfies the given equation. Calculate the real solutions of the equation as follows.
(x1)3+8=0
(x1)3+88=08...Subtract 8 from both sides.
(x1)3=8
(x1)3=(2)3...Write -8 as cube of -2.
(x1)33=(2)33...Take cube root on both sides.
(x-1)=(-2)...Use ann=a.
(x-1)+1=(-2)+1... Add 1 on both sides.
x=-1
Hence, the real solution of the given equation (x1)3+8=0 is x=-1.

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