What are the solutions to the equation 9x^2-6x=1 ?

The solutions to the equation 9x^2-6x=1 are x=(1+sqrt(2))/3 ,x=(1-sqrt(2))/3

Find the zeros of 9x^2-6x=1

The zeros of 9x^2-6x=1 are x=(1+sqrt(2))/3 ,x=(1-sqrt(2))/3

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9 x^{2} - 6 x = 1

x = \frac{1 + 2}{3}, x = \frac{1 - 2}{3}

Decimal Notation

x = 0.80473 \dots, x = - 0.13807 \dots

Solution steps

9 x^{2} - 6 x = 1

Move

1

to the left side

9 x^{2} - 6 x - 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 6 ) \pm ( - 6 ) ^{2} - 4 \cdot 9 ( - 1 )}{2 \cdot 9}

(- 6)^{2} - 4 \cdot 9 (- 1) = 62

x_{1, 2} = \frac{- ( - 6 ) \pm 6 2}{2 \cdot 9}

Separate the solutions

x_{1} = \frac{- ( - 6 ) + 6 2}{2 \cdot 9}, x_{2} = \frac{- ( - 6 ) - 6 2}{2 \cdot 9}

x = \frac{- ( - 6 ) + 6 2}{2 \cdot 9} : \frac{1 + 2}{3}

x = \frac{- ( - 6 ) - 6 2}{2 \cdot 9} : \frac{1 - 2}{3}

The solutions to the quadratic equation are:

x = \frac{1 + 2}{3}, x = \frac{1 - 2}{3}

x^{2} + 12 x + 7

a, a^{2} = h^{2} + (\frac{a}{2})^{2}

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

a, a^{2} + 2 b^{2} = 2 a - 1

x^{2} - 64 x = - 3 x^{2} + 16 x

What are the solutions to the equation 9x^2-6x=1 ?
The solutions to the equation 9x^2-6x=1 are x=(1+sqrt(2))/3 ,x=(1-sqrt(2))/3
Find the zeros of 9x^2-6x=1
The zeros of 9x^2-6x=1 are x=(1+sqrt(2))/3 ,x=(1-sqrt(2))/3