What are the solutions to the equation 9x^2-18x-23=0 ?

The solutions to the equation 9x^2-18x-23=0 are x=(3+4sqrt(2))/3 ,x=(3-4sqrt(2))/3

Find the zeros of 9x^2-18x-23=0

The zeros of 9x^2-18x-23=0 are x=(3+4sqrt(2))/3 ,x=(3-4sqrt(2))/3

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9 x^{2} - 18 x - 23 = 0

x = \frac{3 + 4 2}{3}, x = \frac{3 - 4 2}{3}

Decimal Notation

x = 2.88561 \dots, x = - 0.88561 \dots

Solution steps

9 x^{2} - 18 x - 23 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 18 ) \pm ( - 18 ) ^{2} - 4 \cdot 9 ( - 23 )}{2 \cdot 9}

(- 18)^{2} - 4 \cdot 9 (- 23) = 242

x_{1, 2} = \frac{- ( - 18 ) \pm 24 2}{2 \cdot 9}

Separate the solutions

x_{1} = \frac{- ( - 18 ) + 24 2}{2 \cdot 9}, x_{2} = \frac{- ( - 18 ) - 24 2}{2 \cdot 9}

x = \frac{- ( - 18 ) + 24 2}{2 \cdot 9} : \frac{3 + 4 2}{3}

x = \frac{- ( - 18 ) - 24 2}{2 \cdot 9} : \frac{3 - 4 2}{3}

The solutions to the quadratic equation are:

x = \frac{3 + 4 2}{3}, x = \frac{3 - 4 2}{3}

x^{3} + 3 = x^{3} + x^{2} - 5

x^{2} + 6 x = 27

(x + 5)^{2} + 6 = 2 (x + 4) (x + 2)

2 (x^{2} - 5) = - x^{2} - 1

(x - 1) (2 x + 1) = - 1

What are the solutions to the equation 9x^2-18x-23=0 ?
The solutions to the equation 9x^2-18x-23=0 are x=(3+4sqrt(2))/3 ,x=(3-4sqrt(2))/3
Find the zeros of 9x^2-18x-23=0
The zeros of 9x^2-18x-23=0 are x=(3+4sqrt(2))/3 ,x=(3-4sqrt(2))/3