Solve by Graphing (x-3)^4=0

${(x - 3)}^{4} = 0$

Step 1

Simplify ${(x - 3)}^{4}$ .

Use the Binomial Theorem.

$x^{4} + 4 x^{3} \cdot - 3 + 6 x^{2} {(- 3)}^{2} + 4 x {(- 3)}^{3} + {(- 3)}^{4} = 0$

Simplify each term.

Multiply $- 3$ by $4$ .

$x^{4} - 12 x^{3} + 6 x^{2} {(- 3)}^{2} + 4 x {(- 3)}^{3} + {(- 3)}^{4} = 0$

Raise $- 3$ to the power of $2$ .

$x^{4} - 12 x^{3} + 6 x^{2} \cdot 9 + 4 x {(- 3)}^{3} + {(- 3)}^{4} = 0$

Multiply $9$ by $6$ .

$x^{4} - 12 x^{3} + 54 x^{2} + 4 x {(- 3)}^{3} + {(- 3)}^{4} = 0$

Raise $- 3$ to the power of $3$ .

$x^{4} - 12 x^{3} + 54 x^{2} + 4 x \cdot - 27 + {(- 3)}^{4} = 0$

Multiply $- 27$ by $4$ .

$x^{4} - 12 x^{3} + 54 x^{2} - 108 x + {(- 3)}^{4} = 0$

Raise $- 3$ to the power of $4$ .

$x^{4} - 12 x^{3} + 54 x^{2} - 108 x + 81 = 0$

Step 2

Graph each side of the equation. The solution is the x-value of the point of intersection.

$x = 3$

Step 3