What are the solutions to the equation x^2+sqrt(2)x= 1/2 ?

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

Find the zeros of x^2+sqrt(2)x= 1/2

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

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

x = \frac{- 2 + 2}{2}, x = - \frac{2 + 1}{2}

Decimal Notation

x = 0.29289 \dots, x = - 1.70710 \dots

Solution steps

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

Multiply both sides by

2

2 x^{2} + 22 x = 1

Move

1

to the left side

2 x^{2} + 22 x - 1 = 0

Solve with the quadratic formula

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

(22)^{2} - 4 \cdot 2 (- 1) = 4

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

Separate the solutions

x_{1} = \frac{- 2 2 + 4}{2 \cdot 2}, x_{2} = \frac{- 2 2 - 4}{2 \cdot 2}

x = \frac{- 2 2 + 4}{2 \cdot 2} : \frac{- 2 + 2}{2}

x = \frac{- 2 2 - 4}{2 \cdot 2} : - \frac{2 + 1}{2}

The solutions to the quadratic equation are:

x = \frac{- 2 + 2}{2}, x = - \frac{2 + 1}{2}

d^{2} - 10 d + 5 = 0

2 x + 66 + x = 3 x + 2 + 2 x (4 x)

7 x^{2} - 7 = 0

x^{2} - 2 x + 25 = 0

- 5 x^{2} + 8 x - 1 = 0

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