What are the solutions to the equation -1/2 x^2+9/4 x-1=0 ?

The solutions to the equation -1/2 x^2+9/4 x-1=0 are x= 1/2 ,x=4

Find the zeros of -1/2 x^2+9/4 x-1=0

The zeros of -1/2 x^2+9/4 x-1=0 are x= 1/2 ,x=4

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- \frac{1}{2} x^{2} + \frac{9}{4} x - 1 = 0

x = \frac{1}{2}, x = 4

Solution steps

- \frac{1}{2} x^{2} + \frac{9}{4} x - 1 = 0

Find Least Common Multiplier of

2, 4 : 4

Multiply by LCM=

4

- \frac{1}{2} x^{2} \cdot 4 + \frac{9}{4} x \cdot 4 - 1 \cdot 4 = 0 \cdot 4

Simplify

- 2 x^{2} + 9 x - 4 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 9 \pm 9 ^{2} - 4 ( - 2 ) ( - 4 )}{2 ( - 2 )}

9^{2} - 4 (- 2) (- 4) = 7

x_{1, 2} = \frac{- 9 \pm 7}{2 ( - 2 )}

Separate the solutions

x_{1} = \frac{- 9 + 7}{2 ( - 2 )}, x_{2} = \frac{- 9 - 7}{2 ( - 2 )}

x = \frac{- 9 + 7}{2 ( - 2 )} : \frac{1}{2}

x = \frac{- 9 - 7}{2 ( - 2 )} : 4

The solutions to the quadratic equation are:

x = \frac{1}{2}, x = 4

\frac{9 x ^{4} y ^{2}}{6 x ^{8} y}

3 x^{3} - 3 x^{2} - 18 x

2 x^{2} - 13 x - 7 = 0

9 - 10 r^{2} = - 931

\frac{1}{3} \cdot 3

What are the solutions to the equation -1/2 x^2+9/4 x-1=0 ?
The solutions to the equation -1/2 x^2+9/4 x-1=0 are x= 1/2 ,x=4
Find the zeros of -1/2 x^2+9/4 x-1=0
The zeros of -1/2 x^2+9/4 x-1=0 are x= 1/2 ,x=4