What are the solutions to the equation x^2+x= 11/4 ?

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

Find the zeros of x^2+x= 11/4

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

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x^{2} + x = \frac{11}{4}

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

Decimal Notation

x = 1.23205 \dots, x = - 2.23205 \dots

Solution steps

x^{2} + x = \frac{11}{4}

Multiply both sides by

4

4 x^{2} + 4 x = 11

Move

11

to the left side

4 x^{2} + 4 x - 11 = 0

Solve with the quadratic formula

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

4^{2} - 4 \cdot 4 (- 11) = 83

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

Separate the solutions

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

x = \frac{- 4 + 8 3}{2 \cdot 4} : \frac{- 1 + 2 3}{2}

x = \frac{- 4 - 8 3}{2 \cdot 4} : - \frac{1 + 2 3}{2}

The solutions to the quadratic equation are:

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

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

2 x^{2} + 3 x + 5

(x - 1)^{2} + 1 = 0

w^{2} - 4 w = 12

2 x^{2} + 3 x + 1

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