What are the solutions to the equation 4x^2+4x+1=75 ?

The solutions to the equation 4x^2+4x+1=75 are x=(-1+5sqrt(3))/2 ,x=-(1+5sqrt(3))/2

Find the zeros of 4x^2+4x+1=75

The zeros of 4x^2+4x+1=75 are x=(-1+5sqrt(3))/2 ,x=-(1+5sqrt(3))/2

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4 x^{2} + 4 x + 1 = 75

x = \frac{- 1 + 5 3}{2}, x = - \frac{1 + 5 3}{2}

Decimal Notation

x = 3.83012 \dots, x = - 4.83012 \dots

Solution steps

4 x^{2} + 4 x + 1 = 75

Move

75

to the left side

4 x^{2} + 4 x - 74 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 4 \pm 4 ^{2} - 4 \cdot 4 ( - 74 )}{2 \cdot 4}

4^{2} - 4 \cdot 4 (- 74) = 203

x_{1, 2} = \frac{- 4 \pm 20 3}{2 \cdot 4}

Separate the solutions

x_{1} = \frac{- 4 + 20 3}{2 \cdot 4}, x_{2} = \frac{- 4 - 20 3}{2 \cdot 4}

x = \frac{- 4 + 20 3}{2 \cdot 4} : \frac{- 1 + 5 3}{2}

x = \frac{- 4 - 20 3}{2 \cdot 4} : - \frac{1 + 5 3}{2}

The solutions to the quadratic equation are:

x = \frac{- 1 + 5 3}{2}, x = - \frac{1 + 5 3}{2}

x^{2} + x^{2} = 16

a^{2} - 2 a - 15 = 0

4 x^{2} + 4 x

y^{2} - 5 y - 24 = 0

x^{2} = 5 - 9 x

What are the solutions to the equation 4x^2+4x+1=75 ?
The solutions to the equation 4x^2+4x+1=75 are x=(-1+5sqrt(3))/2 ,x=-(1+5sqrt(3))/2
Find the zeros of 4x^2+4x+1=75
The zeros of 4x^2+4x+1=75 are x=(-1+5sqrt(3))/2 ,x=-(1+5sqrt(3))/2