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

The solutions to the equation 1/2 x^2+x-1=0 are x=-1+sqrt(3),x=-1-sqrt(3)

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

The zeros of 1/2 x^2+x-1=0 are x=-1+sqrt(3),x=-1-sqrt(3)

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

x = - 1 + 3, x = - 1 - 3

Decimal Notation

x = 0.73205 \dots, x = - 2.73205 \dots

Solution steps

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

Multiply both sides by

2

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

Solve with the quadratic formula

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

2^{2} - 4 \cdot 1 \cdot (- 2) = 23

x_{1, 2} = \frac{- 2 \pm 2 3}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- 2 + 2 3}{2 \cdot 1}, x_{2} = \frac{- 2 - 2 3}{2 \cdot 1}

x = \frac{- 2 + 2 3}{2 \cdot 1} : - 1 + 3

x = \frac{- 2 - 2 3}{2 \cdot 1} : - 1 - 3

The solutions to the quadratic equation are:

x = - 1 + 3, x = - 1 - 3

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

x, m x^{2} + 2 m x = 3 x^{2} + m + 1

(3 x - 4)^{2} + (2 x - 3) (x + 5) = - (x^{2} + x + 3)

(3 - x) (- 3 - x) + 10 = 0

12 x^{2} + 48 x + 45 = 0

What are the solutions to the equation 1/2 x^2+x-1=0 ?
The solutions to the equation 1/2 x^2+x-1=0 are x=-1+sqrt(3),x=-1-sqrt(3)
Find the zeros of 1/2 x^2+x-1=0
The zeros of 1/2 x^2+x-1=0 are x=-1+sqrt(3),x=-1-sqrt(3)