What are the solutions to the equation log_{10}(5)(x^2+10x+1)=2 ?

The solutions to the equation log_{10}(5)(x^2+10x+1)=2 are

Find the zeros of log_{10}(5)(x^2+10x+1)=2

The zeros of log_{10}(5)(x^2+10x+1)=2 are

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lo g_{10} (5) (x^{2} + 10 x + 1) = 2

x = \frac{- 10 lo g _{10} ( 5 ) + 96 lo g _{10} ( 5 ) ^{2} + 8 lo g _{10} ( 5 )}{2 lo g _{10} ( 5 )}, x = \frac{- 10 lo g _{10} ( 5 ) - 96 lo g _{10} ( 5 ) ^{2} + 8 lo g _{10} ( 5 )}{2 lo g _{10} ( 5 )}

Decimal Notation

x = 0.18279 \dots, x = - 10.18279 \dots

Solution steps

lo g_{10} (5) (x^{2} + 10 x + 1) = 2

Expand

lo g_{10} (5) (x^{2} + 10 x + 1) : lo g_{10} (5) x^{2} + 10 lo g_{10} (5) x + lo g_{10} (5)

lo g_{10} (5) x^{2} + 10 lo g_{10} (5) x + lo g_{10} (5) = 2

Move

2

to the left side

lo g_{10} (5) x^{2} + 10 lo g_{10} (5) x + lo g_{10} (5) - 2 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 10 lo g _{10} ( 5 ) \pm ( 10 lo g _{10} ( 5 ) ) ^{2} - 4 lo g _{10} ( 5 ) ( lo g _{10} ( 5 ) - 2 )}{2 lo g _{10} ( 5 )}

(10 lo g_{10} (5))^{2} - 4 lo g_{10} (5) (lo g_{10} (5) - 2) = 96 lo g_{10} (5)^{2} + 8 lo g_{10} (5)

x_{1, 2} = \frac{- 10 lo g _{10} ( 5 ) \pm 96 lo g _{10} ( 5 ) ^{2} + 8 lo g _{10} ( 5 )}{2 lo g _{10} ( 5 )}

Separate the solutions

x_{1} = \frac{- 10 lo g _{10} ( 5 ) + 96 lo g _{10} ( 5 ) ^{2} + 8 lo g _{10} ( 5 )}{2 lo g _{10} ( 5 )}, x_{2} = \frac{- 10 lo g _{10} ( 5 ) - 96 lo g _{10} ( 5 ) ^{2} + 8 lo g _{10} ( 5 )}{2 lo g _{10} ( 5 )}

x = \frac{- 10 lo g _{10} ( 5 ) + 96 lo g _{10} ( 5 ) ^{2} + 8 lo g _{10} ( 5 )}{2 lo g _{10} ( 5 )}

x = \frac{- 10 lo g _{10} ( 5 ) - 96 lo g _{10} ( 5 ) ^{2} + 8 lo g _{10} ( 5 )}{2 lo g _{10} ( 5 )}

The solutions to the quadratic equation are:

x = \frac{- 10 lo g _{10} ( 5 ) + 96 lo g _{10} ( 5 ) ^{2} + 8 lo g _{10} ( 5 )}{2 lo g _{10} ( 5 )}, x = \frac{- 10 lo g _{10} ( 5 ) - 96 lo g _{10} ( 5 ) ^{2} + 8 lo g _{10} ( 5 )}{2 lo g _{10} ( 5 )}

x^{2} + 20 = 9 x

2 x^{2} + 8 x + 11

x^{2} + 4 = 16

3 x^{2} - 36 x + 105 = 0

k^{2} + 2 k + 2 = 0

What are the solutions to the equation log_{10}(5)(x^2+10x+1)=2 ?
The solutions to the equation log_{10}(5)(x^2+10x+1)=2 are
Find the zeros of log_{10}(5)(x^2+10x+1)=2
The zeros of log_{10}(5)(x^2+10x+1)=2 are