What are the solutions to the equation (x-7)^4=(x-7)^5 ?

The solutions to the equation (x-7)^4=(x-7)^5 are x=7,x=8

Find the zeros of (x-7)^4=(x-7)^5

The zeros of (x-7)^4=(x-7)^5 are x=7,x=8

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(x - 7)^{4} = (x - 7)^{5}

x = 7, x = 8

Solution steps

(x - 7)^{4} = (x - 7)^{5}

Expand

(x - 7)^{4} : x^{4} - 28 x^{3} + 294 x^{2} - 1372 x + 2401

Expand

(x - 7)^{5} : x^{5} - 35 x^{4} + 490 x^{3} - 3430 x^{2} + 12005 x - 16807

x^{4} - 28 x^{3} + 294 x^{2} - 1372 x + 2401 = x^{5} - 35 x^{4} + 490 x^{3} - 3430 x^{2} + 12005 x - 16807

Switch sides

x^{5} - 35 x^{4} + 490 x^{3} - 3430 x^{2} + 12005 x - 16807 = x^{4} - 28 x^{3} + 294 x^{2} - 1372 x + 2401

Subtract

x^{4} - 28 x^{3} + 294 x^{2} - 1372 x + 2401

from both sides

x^{5} - 35 x^{4} + 490 x^{3} - 3430 x^{2} + 12005 x - 16807 - (x^{4} - 28 x^{3} + 294 x^{2} - 1372 x + 2401) = x^{4} - 28 x^{3} + 294 x^{2} - 1372 x + 2401 - (x^{4} - 28 x^{3} + 294 x^{2} - 1372 x + 2401)

Simplify

x^{5} - 36 x^{4} + 518 x^{3} - 3724 x^{2} + 13377 x - 19208 = 0

Factor

x^{5} - 36 x^{4} + 518 x^{3} - 3724 x^{2} + 13377 x - 19208 : (x - 7)^{4} (x - 8)

(x - 7)^{4} (x - 8) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 7 = 0 or x - 8 = 0

Solve

x - 7 = 0 : x = 7

Solve

x - 8 = 0 : x = 8

The solutions are

x = 7, x = 8

x^{3} = - 125

(x + 5) (x^{2} - 4) = 0

(x^{2} - 5 x)^{2} - 7 (x^{2} - 5 x) + 6 = 0

n^{3} - n - 990 = 0

x^{3} - 3 x^{2} - 25 x + 75 = 0

What are the solutions to the equation (x-7)^4=(x-7)^5 ?
The solutions to the equation (x-7)^4=(x-7)^5 are x=7,x=8
Find the zeros of (x-7)^4=(x-7)^5
The zeros of (x-7)^4=(x-7)^5 are x=7,x=8