Solve by Graphing (x-4)^4-80=0

${(x - 4)}^{4} - 80 = 0$

Step 1

Simplify ${(x - 4)}^{4} - 80$ .

Simplify each term.

Use the Binomial Theorem.

$x^{4} + 4 x^{3} \cdot - 4 + 6 x^{2} {(- 4)}^{2} + 4 x {(- 4)}^{3} + {(- 4)}^{4} - 80 = 0$

Simplify each term.

Multiply $- 4$ by $4$ .

$x^{4} - 16 x^{3} + 6 x^{2} {(- 4)}^{2} + 4 x {(- 4)}^{3} + {(- 4)}^{4} - 80 = 0$

Raise $- 4$ to the power of $2$ .

$x^{4} - 16 x^{3} + 6 x^{2} \cdot 16 + 4 x {(- 4)}^{3} + {(- 4)}^{4} - 80 = 0$

Multiply $16$ by $6$ .

$x^{4} - 16 x^{3} + 96 x^{2} + 4 x {(- 4)}^{3} + {(- 4)}^{4} - 80 = 0$

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

$x^{4} - 16 x^{3} + 96 x^{2} + 4 x \cdot - 64 + {(- 4)}^{4} - 80 = 0$

Multiply $- 64$ by $4$ .

$x^{4} - 16 x^{3} + 96 x^{2} - 256 x + {(- 4)}^{4} - 80 = 0$

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

$x^{4} - 16 x^{3} + 96 x^{2} - 256 x + 256 - 80 = 0$

Subtract $80$ from $256$ .

$x^{4} - 16 x^{3} + 96 x^{2} - 256 x + 176 = 0$

Step 2

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

$x \approx 1.00930243, 6.99069756$

Step 3