What are the solutions to the equation completesquare 5x^2-10x+3 ?

The solutions to the equation completesquare 5x^2-10x+3 are 5(x-1)^2-2

Find the zeros of completesquare 5x^2-10x+3

The zeros of completesquare 5x^2-10x+3 are 5(x-1)^2-2

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complete the square

5 x^{2} - 10 x + 3

5 (x - 1)^{2} - 2

Solution steps

5 x^{2} - 10 x + 3

Write

5 x^{2} - 10 x + 3

in the form:

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

Factor out

5

5 (x^{2} - 2 x + \frac{3}{5})

2 a = - 2 : a = - 1

Add and subtract

(- 1)^{2}

5 (x^{2} - 2 x + \frac{3}{5} + (- 1)^{2} - (- 1)^{2})

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

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

5 ((x - 1)^{2} + \frac{3}{5} - (- 1)^{2})

Simplify

5 (x - 1)^{2} - 2

(7 x + 8) (2 x - 11) = 0

x^{2} - 5 = - 4

A, B = A^{2} - 3 A + 21

(2 x + 3)^{2} + (x + 4)^{2} = 10

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

What are the solutions to the equation completesquare 5x^2-10x+3 ?
The solutions to the equation completesquare 5x^2-10x+3 are 5(x-1)^2-2
Find the zeros of completesquare 5x^2-10x+3
The zeros of completesquare 5x^2-10x+3 are 5(x-1)^2-2