What are the solutions to the equation completesquare x^2-3x+6 ?

The solutions to the equation completesquare x^2-3x+6 are (x-3/2)^2+15/4

Find the zeros of completesquare x^2-3x+6

The zeros of completesquare x^2-3x+6 are (x-3/2)^2+15/4

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complete the square

x^{2} - 3 x + 6

(x - \frac{3}{2})^{2} + \frac{15}{4}

Solution steps

x^{2} - 3 x + 6

Write

x^{2} - 3 x + 6

in the form:

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

2 a = - 3 : a = - \frac{3}{2}

Add and subtract

(- \frac{3}{2})^{2}

x^{2} - 3 x + 6 + (- \frac{3}{2})^{2} - (- \frac{3}{2})^{2}

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

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

(x - \frac{3}{2})^{2} + 6 - (- \frac{3}{2})^{2}

Simplify

(x - \frac{3}{2})^{2} + \frac{15}{4}

(x - 4) (x + 5) = - 18

5 n^{2} + 3 n - 36 = 0

3 x^{2} - 10 x - 13 = 0

3 x^{2} + 41 x + n = 0

x^{2} + x - 50 = 0

What are the solutions to the equation completesquare x^2-3x+6 ?
The solutions to the equation completesquare x^2-3x+6 are (x-3/2)^2+15/4
Find the zeros of completesquare x^2-3x+6
The zeros of completesquare x^2-3x+6 are (x-3/2)^2+15/4