What are the solutions to the equation completesquare z^2+6z+10 ?

The solutions to the equation completesquare z^2+6z+10 are (z+3)^2+1

Find the zeros of completesquare z^2+6z+10

The zeros of completesquare z^2+6z+10 are (z+3)^2+1

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complete the square

z^{2} + 6 z + 10

(z + 3)^{2} + 1

Solution steps

z^{2} + 6 z + 10

Write

z^{2} + 6 z + 10

in the form:

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

2 a = 6 : a = 3

Add and subtract

3^{2}

z^{2} + 6 z + 10 + 3^{2} - 3^{2}

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

z^{2} + 6 z + 3^{2} = (z + 3)^{2}

(z + 3)^{2} + 10 - 3^{2}

Simplify

(z + 3)^{2} + 1

2 v^{2} + 5 v = 7

2 x^{2} - 12 = - 15

(- x + 4)^{2} = 40

0.00029 = \frac{4 π \cdot 1 0 ^{- 7} \cdot x ^{2} \cdot 12.25}{4}

\frac{x ^{2}}{4} = 83

What are the solutions to the equation completesquare z^2+6z+10 ?
The solutions to the equation completesquare z^2+6z+10 are (z+3)^2+1
Find the zeros of completesquare z^2+6z+10
The zeros of completesquare z^2+6z+10 are (z+3)^2+1