What are the solutions to the equation 1/2 x^2-x-6=0 ?

The solutions to the equation 1/2 x^2-x-6=0 are x=1+sqrt(13),x=1-sqrt(13)

Find the zeros of 1/2 x^2-x-6=0

The zeros of 1/2 x^2-x-6=0 are x=1+sqrt(13),x=1-sqrt(13)

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\frac{1}{2} x^{2} - x - 6 = 0

x = 1 + 13, x = 1 - 13

Decimal Notation

x = 4.60555 \dots, x = - 2.60555 \dots

Solution steps

\frac{1}{2} x^{2} - x - 6 = 0

Multiply both sides by

2

x^{2} - 2 x - 12 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 2 ) \pm ( - 2 ) ^{2} - 4 \cdot 1 \cdot ( - 12 )}{2 \cdot 1}

(- 2)^{2} - 4 \cdot 1 \cdot (- 12) = 213

x_{1, 2} = \frac{- ( - 2 ) \pm 2 13}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 2 13}{2 \cdot 1}, x_{2} = \frac{- ( - 2 ) - 2 13}{2 \cdot 1}

x = \frac{- ( - 2 ) + 2 13}{2 \cdot 1} : 1 + 13

x = \frac{- ( - 2 ) - 2 13}{2 \cdot 1} : 1 - 13

The solutions to the quadratic equation are:

x = 1 + 13, x = 1 - 13

∣ x - 4 ∣ < 0.01

- x^{3} + 7 x^{2} + 9 x > 63

4 x^{2} - 24 x + 20 = 0

\frac{2 - 5}{2 + 5}

- 3 (z + 4)^{2} = - 108

What are the solutions to the equation 1/2 x^2-x-6=0 ?
The solutions to the equation 1/2 x^2-x-6=0 are x=1+sqrt(13),x=1-sqrt(13)
Find the zeros of 1/2 x^2-x-6=0
The zeros of 1/2 x^2-x-6=0 are x=1+sqrt(13),x=1-sqrt(13)