What are the solutions to the equation completesquare b^2+19b ?

The solutions to the equation completesquare b^2+19b are (b+19/2)^2-361/4

Find the zeros of completesquare b^2+19b

The zeros of completesquare b^2+19b are (b+19/2)^2-361/4

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complete the square

b^{2} + 19 b

(b + \frac{19}{2})^{2} - \frac{361}{4}

Solution steps

b^{2} + 19 b

Write

b^{2} + 19 b

in the form:

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

2 a = 19 : a = \frac{19}{2}

Add and subtract

(\frac{19}{2})^{2}

b^{2} + 19 b + (\frac{19}{2})^{2} - (\frac{19}{2})^{2}

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

b^{2} + 19 b + (\frac{19}{2})^{2} = (b + \frac{19}{2})^{2}

(b + \frac{19}{2})^{2} - (\frac{19}{2})^{2}

Simplify

(b + \frac{19}{2})^{2} - \frac{361}{4}

x^{2} - 6 x = 0

x, \frac{x ^{2}}{4} + \frac{y ^{2}}{9} - \frac{z ^{2}}{25} = 0

x, z = x^{2} - 4 x y + y^{2} - 6 y

x, x^{2} + y^{2} - 12 x + 14 y + 85 = 0

25 w^{2} - 4 = 0

What are the solutions to the equation completesquare b^2+19b ?
The solutions to the equation completesquare b^2+19b are (b+19/2)^2-361/4
Find the zeros of completesquare b^2+19b
The zeros of completesquare b^2+19b are (b+19/2)^2-361/4