What are the solutions to the equation x^2-18x+69=0 ?

The solutions to the equation x^2-18x+69=0 are x=9+2sqrt(3),x=9-2sqrt(3)

Find the zeros of x^2-18x+69=0

The zeros of x^2-18x+69=0 are x=9+2sqrt(3),x=9-2sqrt(3)

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x^{2} - 18 x + 69 = 0

x = 9 + 23, x = 9 - 23

Decimal Notation

x = 12.46410 \dots, x = 5.53589 \dots

Solution steps

x^{2} - 18 x + 69 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 18 ) \pm ( - 18 ) ^{2} - 4 \cdot 1 \cdot 69}{2 \cdot 1}

(- 18)^{2} - 4 \cdot 1 \cdot 69 = 43

x_{1, 2} = \frac{- ( - 18 ) \pm 4 3}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 18 ) + 4 3}{2 \cdot 1}, x_{2} = \frac{- ( - 18 ) - 4 3}{2 \cdot 1}

x = \frac{- ( - 18 ) + 4 3}{2 \cdot 1} : 9 + 23

x = \frac{- ( - 18 ) - 4 3}{2 \cdot 1} : 9 - 23

The solutions to the quadratic equation are:

x = 9 + 23, x = 9 - 23

60 \cdot \frac{1 5 ^{2}}{2 \cdot 0.005}

[(0.2 - 0.01)^{3} + 2] [0. 2^{2} - (0.0 3^{2})^{2}]

0 = 4 x^{2} - 33 x + 63

(\frac{3}{x})^{3}

9 t^{2} - 18 t + 9 = 0

What are the solutions to the equation x^2-18x+69=0 ?
The solutions to the equation x^2-18x+69=0 are x=9+2sqrt(3),x=9-2sqrt(3)
Find the zeros of x^2-18x+69=0
The zeros of x^2-18x+69=0 are x=9+2sqrt(3),x=9-2sqrt(3)