What is the answer to 5^x+5^{x+1}-6/25 =0 ?

The answer to 5^x+5^{x+1}-6/25 =0 is x=-2

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5^x+5^{x+1}-6/25 =0

5^{x} + 5^{x + 1} - \frac{6}{25} = 0

x = - 2

Solution steps

5^{x} + 5^{x + 1} - \frac{6}{25} = 0

Factor

5^{x} + 5^{x + 1} - \frac{6}{25} : 6 \cdot 5^{x} - \frac{6}{25}

6 \cdot 5^{x} - \frac{6}{25} = 0

Add

\frac{6}{25}

to both sides

6 \cdot 5^{x} - \frac{6}{25} + \frac{6}{25} = 0 + \frac{6}{25}

Simplify

6 \cdot 5^{x} = \frac{6}{25}

Divide both sides by

6

5^{x} = \frac{1}{25}

Apply exponent rules

x = - 2

2^{x + 1} + 2^{x} + 2^{x - 1} = 14

7^{x} = 4

6 (6^{2 x}) - 37 (6^{x}) + 6 = 0

e^{2 x} = 3 e^{x}

10 \cdot 3^{\frac{5 t}{4}} = 800

What is the answer to 5^x+5^{x+1}-6/25 =0 ?
The answer to 5^x+5^{x+1}-6/25 =0 is x=-2
Solve for x: 5^x+5^{x+1}-6/25 =0
The solution is x=-2