What are the solutions to the equation 4x^2+1=8x ?

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

Find the zeros of 4x^2+1=8x

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

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4 x^{2} + 1 = 8 x

x = \frac{2 + 3}{2}, x = \frac{2 - 3}{2}

Decimal Notation

x = 1.86602 \dots, x = 0.13397 \dots

Solution steps

4 x^{2} + 1 = 8 x

Move

8 x

to the left side

4 x^{2} + 1 - 8 x = 0

Write in the standard form

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

4 x^{2} - 8 x + 1 = 0

Solve with the quadratic formula

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

(- 8)^{2} - 4 \cdot 4 \cdot 1 = 43

x_{1, 2} = \frac{- ( - 8 ) \pm 4 3}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- ( - 8 ) + 4 3}{2 \cdot 4}, x_{2} = \frac{- ( - 8 ) - 4 3}{2 \cdot 4}

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

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

The solutions to the quadratic equation are:

x = \frac{2 + 3}{2}, x = \frac{2 - 3}{2}

- 1.5 (4 x + 1) \geq 4.5 - 2.5 (x + 1)

8 x^{2} - 10 x - 3 \leq 0

15 0^{2} + 20 0^{2} = c^{2}

8 x^{2} - 18 = 0

3 x + 11 \leq 5

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