What are the solutions to the equation completesquare x^2-3x+9 ?

The solutions to the equation completesquare x^2-3x+9 are (x-3/2)^2+27/4

Find the zeros of completesquare x^2-3x+9

The zeros of completesquare x^2-3x+9 are (x-3/2)^2+27/4

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complete the square

x^{2} - 3 x + 9

(x - \frac{3}{2})^{2} + \frac{27}{4}

Solution steps

x^{2} - 3 x + 9

Write

x^{2} - 3 x + 9

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 + 9 + (- \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} + 9 - (- \frac{3}{2})^{2}

Simplify

(x - \frac{3}{2})^{2} + \frac{27}{4}

x^{2} + 15 x - 16 = 0

2 x^{2} - 9 x - 4 = 0

4 x^{2} + 16 x - 1

2 x^{2} + 10 = 4 x + 16

x^{2} + 2 x + 1 = 36

What are the solutions to the equation completesquare x^2-3x+9 ?
The solutions to the equation completesquare x^2-3x+9 are (x-3/2)^2+27/4
Find the zeros of completesquare x^2-3x+9
The zeros of completesquare x^2-3x+9 are (x-3/2)^2+27/4