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Kobotan [32]
3 years ago
7

Solve the equation

" id="TexFormula1" title="log10 \: ( {x}^{2} - 4x + 7) = 2" alt="log10 \: ( {x}^{2} - 4x + 7) = 2" align="absmiddle" class="latex-formula">

​
Mathematics
1 answer:
tatiyna3 years ago
6 0

Answer:

x = 2 ±sqrt( 97)

Step-by-step explanation:

log10(x^2 -4x+7) =2

Raise each side to the base 10

10 ^ log10(x^2 -4x+7) =10^2

x^2 -4x +7 = 100

Subtract 7 from each side

x^2 -4x+7-7 = 100-7

x^2 -4x = 93

Complete the square

-4/2 = -2  (-2)^2 = 4

Add 4 to each side

x^2 -4x+4 = 93+4

(x-2)^2 = 97

Take the square root of each side

sqrt((x-2)^2 )=±sqrt( 97)

x-2 = ±sqrt( 97)

Add 2 to each side

x = 2 ±sqrt( 97)

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