What are the solutions to the equation roots a^2-d^2+n^2-c^2-2an-2cd ?

The solutions to the equation roots a^2-d^2+n^2-c^2-2an-2cd are c=-d-a+n,c=-d+a-n

Find the zeros of roots a^2-d^2+n^2-c^2-2an-2cd

The zeros of roots a^2-d^2+n^2-c^2-2an-2cd are c=-d-a+n,c=-d+a-n

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roots

a^{2} - d^{2} + n^{2} - c^{2} - 2 an - 2 c d

c = - d - a + n, c = - d + a - n

Solution steps

a^{2} - d^{2} + n^{2} - c^{2} - 2 an - 2 c d

The roots are the intercepts with the x-axis

(y = 0)

a^{2} - d^{2} + n^{2} - c^{2} - 2 an - 2 c d = 0

Write in the standard form

a x^{2} + b x + c = 0

- c^{2} - 2 d c + a^{2} - d^{2} + n^{2} - 2 an = 0

Solve with the quadratic formula

c_{1, 2} = \frac{- ( - 2 d ) \pm ( - 2 d ) ^{2} - 4 ( - 1 ) ( a ^{2} - d ^{2} + n ^{2} - 2 an )}{2 ( - 1 )}

Simplify

(- 2 d)^{2} - 4 (- 1) (a^{2} - d^{2} + n^{2} - 2 an) : 2 (a - n)

c_{1, 2} = \frac{- ( - 2 d ) \pm 2 ( a - n )}{2 ( - 1 )}

Separate the solutions

c_{1} = \frac{- ( - 2 d ) + 2 ( a - n )}{2 ( - 1 )}, c_{2} = \frac{- ( - 2 d ) - 2 ( a - n )}{2 ( - 1 )}

c = \frac{- ( - 2 d ) + 2 ( a - n )}{2 ( - 1 )} : - d - a + n

c = \frac{- ( - 2 d ) - 2 ( a - n )}{2 ( - 1 )} : - d + a - n

The solutions to the quadratic equation are:

c = - d - a + n, c = - d + a - n

\frac{3}{2} (x - 2)^{2} = 72

2 x^{2} - 9 = 121

6 x^{2} + 11 x = - 3

a x^{2} - (4 a + 1) x + 3 a + 3 = 0

2 k^{2} + 5 k + 4 = 1

What are the solutions to the equation roots a^2-d^2+n^2-c^2-2an-2cd ?
The solutions to the equation roots a^2-d^2+n^2-c^2-2an-2cd are c=-d-a+n,c=-d+a-n
Find the zeros of roots a^2-d^2+n^2-c^2-2an-2cd
The zeros of roots a^2-d^2+n^2-c^2-2an-2cd are c=-d-a+n,c=-d+a-n