What are the solutions to the equation 1/2 a^2-a-5/2 =0 ?

The solutions to the equation 1/2 a^2-a-5/2 =0 are a=1+sqrt(6),a=1-sqrt(6)

Find the zeros of 1/2 a^2-a-5/2 =0

The zeros of 1/2 a^2-a-5/2 =0 are a=1+sqrt(6),a=1-sqrt(6)

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\frac{1}{2} a^{2} - a - \frac{5}{2} = 0

a = 1 + 6, a = 1 - 6

Decimal

a = 3.44948 \dots, a = - 1.44948 \dots

Solution steps

\frac{1}{2} a^{2} - a - \frac{5}{2} = 0

Multiply both sides by

2

a^{2} - 2 a - 5 = 0

Solve with the quadratic formula

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

(- 2)^{2} - 4 \cdot 1 \cdot (- 5) = 26

a_{1, 2} = \frac{- ( - 2 ) \pm 2 6}{2 \cdot 1}

Separate the solutions

a_{1} = \frac{- ( - 2 ) + 2 6}{2 \cdot 1}, a_{2} = \frac{- ( - 2 ) - 2 6}{2 \cdot 1}

a = \frac{- ( - 2 ) + 2 6}{2 \cdot 1} : 1 + 6

a = \frac{- ( - 2 ) - 2 6}{2 \cdot 1} : 1 - 6

The solutions to the quadratic equation are:

a = 1 + 6, a = 1 - 6

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

25 b^{2} + 24 b + 9 = - 6 b

5 x^{2} - 31 x - 28 = 0

5 k^{2} - 28 k + 19 = 4

x^{2} + 2 x - 13 = 130

What are the solutions to the equation 1/2 a^2-a-5/2 =0 ?
The solutions to the equation 1/2 a^2-a-5/2 =0 are a=1+sqrt(6),a=1-sqrt(6)
Find the zeros of 1/2 a^2-a-5/2 =0
The zeros of 1/2 a^2-a-5/2 =0 are a=1+sqrt(6),a=1-sqrt(6)