What are the solutions to the equation 1/2 x^2-1/2 x-23/8 =0 ?

The solutions to the equation 1/2 x^2-1/2 x-23/8 =0 are x=(1+2sqrt(6))/2 ,x=(1-2sqrt(6))/2

Find the zeros of 1/2 x^2-1/2 x-23/8 =0

The zeros of 1/2 x^2-1/2 x-23/8 =0 are x=(1+2sqrt(6))/2 ,x=(1-2sqrt(6))/2

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\frac{1}{2} x^{2} - \frac{1}{2} x - \frac{23}{8} = 0

x = \frac{1 + 2 6}{2}, x = \frac{1 - 2 6}{2}

Decimal Notation

x = 2.94948 \dots, x = - 1.94948 \dots

Solution steps

\frac{1}{2} x^{2} - \frac{1}{2} x - \frac{23}{8} = 0

Find Least Common Multiplier of

2, 8 : 8

Multiply by LCM=

8

\frac{1}{2} x^{2} \cdot 8 - \frac{1}{2} x \cdot 8 - \frac{23}{8} \cdot 8 = 0 \cdot 8

Simplify

4 x^{2} - 4 x - 23 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 4 ) \pm ( - 4 ) ^{2} - 4 \cdot 4 ( - 23 )}{2 \cdot 4}

(- 4)^{2} - 4 \cdot 4 (- 23) = 86

x_{1, 2} = \frac{- ( - 4 ) \pm 8 6}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 4 ) + 8 6}{2 \cdot 4}, x_{2} = \frac{- ( - 4 ) - 8 6}{2 \cdot 4}

x = \frac{- ( - 4 ) + 8 6}{2 \cdot 4} : \frac{1 + 2 6}{2}

x = \frac{- ( - 4 ) - 8 6}{2 \cdot 4} : \frac{1 - 2 6}{2}

The solutions to the quadratic equation are:

x = \frac{1 + 2 6}{2}, x = \frac{1 - 2 6}{2}

5 p - 50

- \frac{π}{6} + 2 π

15 j + 2 = 14

\frac{1}{8} + x = \frac{1}{4.8}

54 x^{2} - 24 y^{2}

What are the solutions to the equation 1/2 x^2-1/2 x-23/8 =0 ?
The solutions to the equation 1/2 x^2-1/2 x-23/8 =0 are x=(1+2sqrt(6))/2 ,x=(1-2sqrt(6))/2
Find the zeros of 1/2 x^2-1/2 x-23/8 =0
The zeros of 1/2 x^2-1/2 x-23/8 =0 are x=(1+2sqrt(6))/2 ,x=(1-2sqrt(6))/2