What are the solutions to the equation completesquare x^2-3x+7 ?

The solutions to the equation completesquare x^2-3x+7 are (x-3/2)^2+19/4

Find the zeros of completesquare x^2-3x+7

The zeros of completesquare x^2-3x+7 are (x-3/2)^2+19/4

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complete the square

x^{2} - 3 x + 7

(x - \frac{3}{2})^{2} + \frac{19}{4}

Solution steps

x^{2} - 3 x + 7

Write

x^{2} - 3 x + 7

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 + 7 + (- \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} + 7 - (- \frac{3}{2})^{2}

Simplify

(x - \frac{3}{2})^{2} + \frac{19}{4}

k = \frac{1}{2} m v^{2}

3 (3 x + 4)^{2} + 24 = 36

x (x - 1) = 72

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

3 x^{2} + 12 x + 5 = 0

What are the solutions to the equation completesquare x^2-3x+7 ?
The solutions to the equation completesquare x^2-3x+7 are (x-3/2)^2+19/4
Find the zeros of completesquare x^2-3x+7
The zeros of completesquare x^2-3x+7 are (x-3/2)^2+19/4