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

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

Find the zeros of 2x^2-2x=x^2+2x+1

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

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2 x^{2} - 2 x = x^{2} + 2 x + 1

x = 2 - 5, x = 2 + 5

Decimal Notation

x = - 0.23606 \dots, x = 4.23606 \dots

Solution steps

2 x^{2} - 2 x = x^{2} + 2 x + 1

Switch sides

x^{2} + 2 x + 1 = 2 x^{2} - 2 x

Move

2 x

to the left side

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

Move

2 x^{2}

to the left side

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

Solve with the quadratic formula

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

4^{2} - 4 (- 1) \cdot 1 = 25

x_{1, 2} = \frac{- 4 \pm 2 5}{2 ( - 1 )}

Separate the solutions

x_{1} = \frac{- 4 + 2 5}{2 ( - 1 )}, x_{2} = \frac{- 4 - 2 5}{2 ( - 1 )}

x = \frac{- 4 + 2 5}{2 ( - 1 )} : 2 - 5

x = \frac{- 4 - 2 5}{2 ( - 1 )} : 2 + 5

The solutions to the quadratic equation are:

x = 2 - 5, x = 2 + 5

3 (x + 2)^{2} + 4 = 40

3 x (2 x + 9) = 10 x

4 x^{2} - 11 x = 7

7 c^{2} = c + 6

4 c^{2} + c - 6 = 0

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