If x^{3}+3x^{2}+3x=7, then x is equal to | vedclass

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(C) Given equation: $x^{3}+3x^{2}+3x=7$To solve for $x$,add $1$ to both sides of the equation to complete the cube:$x^{3}+3x^{2}+3x+1 = 7+1$Recognizin

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$1$

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(C) Given equation: $x^{3}+3x^{2}+3x=7$To solve for $x$,add $1$ to both sides of the equation to complete the cube:$x^{3}+3x^{2}+3x+1 = 7+1$Recognizing the algebraic identity $(a+b)^{3} = a^{3}+3a^{2}b+3ab^{2}+b^{3}$,we can rewrite the left side:$(x+1)^{3} = 8$Since $8 = 2^{3}$,we have:$(x+1)^{3} = 2^{3}$Taking the cube root on both sides:$x+1 = 2$Therefore:$x = 2-1 = 1$

If $x^{3}+3x^{2}+3x=7,$ then $x$ is equal to

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