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

The solutions to the equation 2x^2-x= 1/2 are x=(1+sqrt(5))/4 ,x=(1-sqrt(5))/4

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

The zeros of 2x^2-x= 1/2 are x=(1+sqrt(5))/4 ,x=(1-sqrt(5))/4

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

x = \frac{1 + 5}{4}, x = \frac{1 - 5}{4}

Decimal Notation

x = 0.80901 \dots, x = - 0.30901 \dots

Solution steps

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

Multiply both sides by

2

4 x^{2} - 2 x = 1

Move

1

to the left side

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

Solve with the quadratic formula

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

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

x_{1, 2} = \frac{- ( - 2 ) \pm 2 5}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 2 5}{2 \cdot 4}, x_{2} = \frac{- ( - 2 ) - 2 5}{2 \cdot 4}

x = \frac{- ( - 2 ) + 2 5}{2 \cdot 4} : \frac{1 + 5}{4}

x = \frac{- ( - 2 ) - 2 5}{2 \cdot 4} : \frac{1 - 5}{4}

The solutions to the quadratic equation are:

x = \frac{1 + 5}{4}, x = \frac{1 - 5}{4}

5 q^{2} = 18 q + 8

x^{2} + 7 x + 19 = 0

2 (x - 6)^{2} = 98

5 k^{2} + 6 k + 3 = 0

74 x^{2} + 1 = 10 x

What are the solutions to the equation 2x^2-x= 1/2 ?
The solutions to the equation 2x^2-x= 1/2 are x=(1+sqrt(5))/4 ,x=(1-sqrt(5))/4
Find the zeros of 2x^2-x= 1/2
The zeros of 2x^2-x= 1/2 are x=(1+sqrt(5))/4 ,x=(1-sqrt(5))/4