What are the solutions to the equation x^2-14x+31=0 ?

The solutions to the equation x^2-14x+31=0 are x=7+3sqrt(2),x=7-3sqrt(2)

Find the zeros of x^2-14x+31=0

The zeros of x^2-14x+31=0 are x=7+3sqrt(2),x=7-3sqrt(2)

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x^{2} - 14 x + 31 = 0

x = 7 + 32, x = 7 - 32

Decimal Notation

x = 11.24264 \dots, x = 2.75735 \dots

Solution steps

x^{2} - 14 x + 31 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 14 ) \pm ( - 14 ) ^{2} - 4 \cdot 1 \cdot 31}{2 \cdot 1}

(- 14)^{2} - 4 \cdot 1 \cdot 31 = 62

x_{1, 2} = \frac{- ( - 14 ) \pm 6 2}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 14 ) + 6 2}{2 \cdot 1}, x_{2} = \frac{- ( - 14 ) - 6 2}{2 \cdot 1}

x = \frac{- ( - 14 ) + 6 2}{2 \cdot 1} : 7 + 32

x = \frac{- ( - 14 ) - 6 2}{2 \cdot 1} : 7 - 32

The solutions to the quadratic equation are:

x = 7 + 32, x = 7 - 32

3 a^{2} + 2 a - 5

3 < n and 5 < 32

\frac{4}{5} \cdot \frac{3}{11} \cdot \frac{1}{4}

18 x^{5} y^{4} z^{3} + 30 x^{4} y^{3} z^{5}

14 x z - 18 x z^{2}

What are the solutions to the equation x^2-14x+31=0 ?
The solutions to the equation x^2-14x+31=0 are x=7+3sqrt(2),x=7-3sqrt(2)
Find the zeros of x^2-14x+31=0
The zeros of x^2-14x+31=0 are x=7+3sqrt(2),x=7-3sqrt(2)