What are the solutions to the equation x^2-3/4 x=-1/4 ?

The solutions to the equation x^2-3/4 x=-1/4 are x= 3/8+i(sqrt(7))/8 ,x= 3/8-i(sqrt(7))/8

Find the zeros of x^2-3/4 x=-1/4

The zeros of x^2-3/4 x=-1/4 are x= 3/8+i(sqrt(7))/8 ,x= 3/8-i(sqrt(7))/8

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x^{2} - \frac{3}{4} x = - \frac{1}{4}

x = \frac{3}{8} + i \frac{7}{8}, x = \frac{3}{8} - i \frac{7}{8}

Solution steps

x^{2} - \frac{3}{4} x = - \frac{1}{4}

Multiply both sides by

4

4 x^{2} - 3 x = - 1

Move

1

to the left side

4 x^{2} - 3 x + 1 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 4 \cdot 1}{2 \cdot 4}

Simplify

(- 3)^{2} - 4 \cdot 4 \cdot 1 : 7 i

x_{1, 2} = \frac{- ( - 3 ) \pm 7 i}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 3 ) + 7 i}{2 \cdot 4}, x_{2} = \frac{- ( - 3 ) - 7 i}{2 \cdot 4}

x = \frac{- ( - 3 ) + 7 i}{2 \cdot 4} : \frac{3}{8} + i \frac{7}{8}

x = \frac{- ( - 3 ) - 7 i}{2 \cdot 4} : \frac{3}{8} - i \frac{7}{8}

The solutions to the quadratic equation are:

x = \frac{3}{8} + i \frac{7}{8}, x = \frac{3}{8} - i \frac{7}{8}

8 t^{2} - 64 t + 281 = 0

- 0.5 x^{2} + 15 x = 0

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

6 x^{2} - 6 x + 4 = 0

24 = x^{2} + 2 x

What are the solutions to the equation x^2-3/4 x=-1/4 ?
The solutions to the equation x^2-3/4 x=-1/4 are x= 3/8+i(sqrt(7))/8 ,x= 3/8-i(sqrt(7))/8
Find the zeros of x^2-3/4 x=-1/4
The zeros of x^2-3/4 x=-1/4 are x= 3/8+i(sqrt(7))/8 ,x= 3/8-i(sqrt(7))/8