What are the solutions to the equation completesquare 2x^2-20x+41 ?

The solutions to the equation completesquare 2x^2-20x+41 are 2(x-5)^2-9

Find the zeros of completesquare 2x^2-20x+41

The zeros of completesquare 2x^2-20x+41 are 2(x-5)^2-9

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complete the square

2 x^{2} - 20 x + 41

2 (x - 5)^{2} - 9

Solution steps

2 x^{2} - 20 x + 41

Write

2 x^{2} - 20 x + 41

in the form:

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

Factor out

2

2 (x^{2} - 10 x + \frac{41}{2})

2 a = - 10 : a = - 5

Add and subtract

(- 5)^{2}

2 (x^{2} - 10 x + \frac{41}{2} + (- 5)^{2} - (- 5)^{2})

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

x^{2} - 10 x + (- 5)^{2} = (x - 5)^{2}

2 ((x - 5)^{2} + \frac{41}{2} - (- 5)^{2})

Simplify

2 (x - 5)^{2} - 9

\frac{x ^{2} - 4}{3} - \frac{6 - x}{2} = 3

a^{2} + (- 2 a)^{2} = 4 0^{2}

2 x^{2} - 20 x + 41 = 0

a x^{2}

x^{2} + 4 x + 4

What are the solutions to the equation completesquare 2x^2-20x+41 ?
The solutions to the equation completesquare 2x^2-20x+41 are 2(x-5)^2-9
Find the zeros of completesquare 2x^2-20x+41
The zeros of completesquare 2x^2-20x+41 are 2(x-5)^2-9