What are the solutions to the equation (2x-15)^5=(2x-15)^3 ?

The solutions to the equation (2x-15)^5=(2x-15)^3 are x=7,x=8,x= 15/2

Find the zeros of (2x-15)^5=(2x-15)^3

The zeros of (2x-15)^5=(2x-15)^3 are x=7,x=8,x= 15/2

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(2 x - 15)^{5} = (2 x - 15)^{3}

x = 7, x = 8, x = \frac{15}{2}

Decimal Notation

x = 7, x = 8, x = 7.5

Solution steps

(2 x - 15)^{5} = (2 x - 15)^{3}

Expand

(2 x - 15)^{5} : 32 x^{5} - 1200 x^{4} + 18000 x^{3} - 135000 x^{2} + 506250 x - 759375

Expand

(2 x - 15)^{3} : 8 x^{3} - 180 x^{2} + 1350 x - 3375

32 x^{5} - 1200 x^{4} + 18000 x^{3} - 135000 x^{2} + 506250 x - 759375 = 8 x^{3} - 180 x^{2} + 1350 x - 3375

Subtract

8 x^{3} - 180 x^{2} + 1350 x - 3375

from both sides

32 x^{5} - 1200 x^{4} + 18000 x^{3} - 135000 x^{2} + 506250 x - 759375 - (8 x^{3} - 180 x^{2} + 1350 x - 3375) = 8 x^{3} - 180 x^{2} + 1350 x - 3375 - (8 x^{3} - 180 x^{2} + 1350 x - 3375)

Simplify

32 x^{5} - 1200 x^{4} + 17992 x^{3} - 134820 x^{2} + 504900 x - 756000 = 0

Factor

32 x^{5} - 1200 x^{4} + 17992 x^{3} - 134820 x^{2} + 504900 x - 756000 : 4 (x - 7) (x - 8) (2 x - 15)^{3}

4 (x - 7) (x - 8) (2 x - 15)^{3} = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x - 7 = 0 or x - 8 = 0 or 2 x - 15 = 0

Solve

x - 7 = 0 : x = 7

Solve

x - 8 = 0 : x = 8

Solve

2 x - 15 = 0 : x = \frac{15}{2}

The solutions are

x = 7, x = 8, x = \frac{15}{2}

\frac{x ^{4} + 9}{10} = x^{2}

y^{6} - 10 y^{3} + 16 = 0

5 x^{3} + 45 x = 2 x^{2} + 18

5 X (X + 6)^{2} = 0

3 x^{4} = 1536 x

What are the solutions to the equation (2x-15)^5=(2x-15)^3 ?
The solutions to the equation (2x-15)^5=(2x-15)^3 are x=7,x=8,x= 15/2
Find the zeros of (2x-15)^5=(2x-15)^3
The zeros of (2x-15)^5=(2x-15)^3 are x=7,x=8,x= 15/2