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

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

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

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

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

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

Decimal Notation

w = 3.83012 \dots, w = - 4.83012 \dots

Solution steps

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

Move

75

to the left side

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

Solve with the quadratic formula

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

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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

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

21 + 3 x = - 15

y - 5 (y + 1) \geq 2 y - 5

8 x - 4 = 60

\frac{x ^{3} + 729}{x + 9}

x^{2} - 16 x - 17

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