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

The solutions to the equation 4x^2=2x-3 are x= 1/4+i(sqrt(11))/4 ,x= 1/4-i(sqrt(11))/4

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

The zeros of 4x^2=2x-3 are x= 1/4+i(sqrt(11))/4 ,x= 1/4-i(sqrt(11))/4

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4 x^{2} = 2 x - 3

x = \frac{1}{4} + i \frac{11}{4}, x = \frac{1}{4} - i \frac{11}{4}

Solution steps

4 x^{2} = 2 x - 3

Move

3

to the left side

4 x^{2} + 3 = 2 x

Move

2 x

to the left side

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

Write in the standard form

a x^{2} + b x + c = 0

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

Solve with the quadratic formula

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

Simplify

(- 2)^{2} - 4 \cdot 4 \cdot 3 : 211 i

x_{1, 2} = \frac{- ( - 2 ) \pm 2 11 i}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 2 ) + 2 11 i}{2 \cdot 4}, x_{2} = \frac{- ( - 2 ) - 2 11 i}{2 \cdot 4}

x = \frac{- ( - 2 ) + 2 11 i}{2 \cdot 4} : \frac{1}{4} + i \frac{11}{4}

x = \frac{- ( - 2 ) - 2 11 i}{2 \cdot 4} : \frac{1}{4} - i \frac{11}{4}

The solutions to the quadratic equation are:

x = \frac{1}{4} + i \frac{11}{4}, x = \frac{1}{4} - i \frac{11}{4}

2 x^{3} - x^{2} - 2 x + 1

e^{3 πi}

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

25 b^{2} - 9

4 (x - 5)^{2} - 21 = - 5

What are the solutions to the equation 4x^2=2x-3 ?
The solutions to the equation 4x^2=2x-3 are x= 1/4+i(sqrt(11))/4 ,x= 1/4-i(sqrt(11))/4
Find the zeros of 4x^2=2x-3
The zeros of 4x^2=2x-3 are x= 1/4+i(sqrt(11))/4 ,x= 1/4-i(sqrt(11))/4