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

The solutions to the equation 1/2 x^2-x-2=0 are x=1+sqrt(5),x=1-sqrt(5)

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

The zeros of 1/2 x^2-x-2=0 are x=1+sqrt(5),x=1-sqrt(5)

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

x = 1 + 5, x = 1 - 5

Decimal Notation

x = 3.23606 \dots, x = - 1.23606 \dots

Solution steps

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

Multiply both sides by

2

x^{2} - 2 x - 4 = 0

Solve with the quadratic formula

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

(- 2)^{2} - 4 \cdot 1 \cdot (- 4) = 25

x_{1, 2} = \frac{- ( - 2 ) \pm 2 5}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 2 5}{2 \cdot 1}, x_{2} = \frac{- ( - 2 ) - 2 5}{2 \cdot 1}

x = \frac{- ( - 2 ) + 2 5}{2 \cdot 1} : 1 + 5

x = \frac{- ( - 2 ) - 2 5}{2 \cdot 1} : 1 - 5

The solutions to the quadratic equation are:

x = 1 + 5, x = 1 - 5

(2 x - 1)^{2} - x (x - 3) = 5

(2 x - 7)^{2} - 3 = 0

4 (1 + 4 x) = x (x - 7)

15 x^{2} + 6 x - 14 = 0

x, x^{2} + y^{2} - 3 x y + 4 = 0

What are the solutions to the equation 1/2 x^2-x-2=0 ?
The solutions to the equation 1/2 x^2-x-2=0 are x=1+sqrt(5),x=1-sqrt(5)
Find the zeros of 1/2 x^2-x-2=0
The zeros of 1/2 x^2-x-2=0 are x=1+sqrt(5),x=1-sqrt(5)