What are the solutions to the equation completesquare 1/2 x^2-4x+3 ?

The solutions to the equation completesquare 1/2 x^2-4x+3 are 1/2 (x-4)^2-5

Find the zeros of completesquare 1/2 x^2-4x+3

The zeros of completesquare 1/2 x^2-4x+3 are 1/2 (x-4)^2-5

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complete the square

\frac{1}{2} x^{2} - 4 x + 3

\frac{1}{2} (x - 4)^{2} - 5

Solution steps

\frac{1}{2} x^{2} - 4 x + 3

Write in the standard form

a x^{2} + b x + c

\frac{x ^{2}}{2} - 4 x + 3

Write

\frac{x ^{2}}{2} - 4 x + 3

in the form:

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

Factor out

\frac{1}{2}

\frac{1}{2} (x^{2} - 8 x + 6)

2 a = - 8 : a = - 4

Add and subtract

(- 4)^{2}

\frac{1}{2} (x^{2} - 8 x + 6 + (- 4)^{2} - (- 4)^{2})

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

x^{2} - 8 x + (- 4)^{2} = (x - 4)^{2}

\frac{1}{2} ((x - 4)^{2} + 6 - (- 4)^{2})

Simplify

\frac{1}{2} (x - 4)^{2} - 5

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

- 11 x + 5 + 2 x^{2} = 0

7 - 4 (y + 3) - (y + 3)^{2} = 0

2 x^{2} - 7 x - 3 = 0

p^{2} - 10 = 3 p

What are the solutions to the equation completesquare 1/2 x^2-4x+3 ?
The solutions to the equation completesquare 1/2 x^2-4x+3 are 1/2 (x-4)^2-5
Find the zeros of completesquare 1/2 x^2-4x+3
The zeros of completesquare 1/2 x^2-4x+3 are 1/2 (x-4)^2-5