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

The solutions to the equation completesquare 2x^2+2x+1 are 2(x+1/2)^2+1/2

Find the zeros of completesquare 2x^2+2x+1

The zeros of completesquare 2x^2+2x+1 are 2(x+1/2)^2+1/2

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complete the square

2 x^{2} + 2 x + 1

2 (x + \frac{1}{2})^{2} + \frac{1}{2}

Solution steps

2 x^{2} + 2 x + 1

Write

2 x^{2} + 2 x + 1

in the form:

x^{2} + 2 a x + a^{2}

Factor out

2

2 (x^{2} + x + \frac{1}{2})

2 a = 1 : a = \frac{1}{2}

Add and subtract

(\frac{1}{2})^{2}

2 (x^{2} + x + \frac{1}{2} + (\frac{1}{2})^{2} - (\frac{1}{2})^{2})

x^{2} + 2 a x + a^{2} = (x + a)^{2}

x^{2} + 1 x + (\frac{1}{2})^{2} = (x + \frac{1}{2})^{2}

2 ((x + \frac{1}{2})^{2} + \frac{1}{2} - (\frac{1}{2})^{2})

Simplify

2 (x + \frac{1}{2})^{2} + \frac{1}{2}

8^{2} + 3^{2} = c^{2}

- k^{2} - 65 k + 720 = 0

- 16 x^{2} + 85 x = 0

x^{2} - 7 x = 0

3 x^{2} - 42 x = 120

What are the solutions to the equation completesquare 2x^2+2x+1 ?
The solutions to the equation completesquare 2x^2+2x+1 are 2(x+1/2)^2+1/2
Find the zeros of completesquare 2x^2+2x+1
The zeros of completesquare 2x^2+2x+1 are 2(x+1/2)^2+1/2