What are the solutions to the equation 4x^2+9=4x ?

The solutions to the equation 4x^2+9=4x are x= 1/2+sqrt(2)i,x= 1/2-sqrt(2)i

Find the zeros of 4x^2+9=4x

The zeros of 4x^2+9=4x are x= 1/2+sqrt(2)i,x= 1/2-sqrt(2)i

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4 x^{2} + 9 = 4 x

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

Solution steps

4 x^{2} + 9 = 4 x

Move

4 x

to the left side

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

Write in the standard form

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

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

Solve with the quadratic formula

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

Simplify

(- 4)^{2} - 4 \cdot 4 \cdot 9 : 82 i

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

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

\frac{1}{4} - x + \frac{3}{6} + x = 0

\frac{3 x - 1}{4} - \frac{2 x + 3}{2} < - 2

x^{2} > 36

4 x^{2} + 4 x + 37 = 0

\frac{2}{3} x^{2} - 1 \geq 0

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