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

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

Find the zeros of x*x+4=x+2*x+1

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

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x \cdot x + 4 = x + 2 \cdot x + 1

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

Solution steps

xx + 4 = x + 2 x + 1

Expand

xx + 4 : x^{2} + 4

x^{2} + 4 = 3 x + 1

Move

1

to the left side

x^{2} + 3 = 3 x

Move

3 x

to the left side

x^{2} + 3 - 3 x = 0

Write in the standard form

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

x^{2} - 3 x + 3 = 0

Solve with the quadratic formula

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

Simplify

(- 3)^{2} - 4 \cdot 1 \cdot 3 : 3 i

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

Separate the solutions

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

x = \frac{- ( - 3 ) + 3 i}{2 \cdot 1} : \frac{3}{2} + i \frac{3}{2}

x = \frac{- ( - 3 ) - 3 i}{2 \cdot 1} : \frac{3}{2} - i \frac{3}{2}

The solutions to the quadratic equation are:

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

x^{2} - 2 x - 35 = 0

25 x^{2} + 9 x^{2} = 225

x^{2} - 6.4 x = - 1.24

x, z = x^{2} + 2 y^{2}

3 r^{2} + 6 r + 1 = 0

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