What are the solutions to the equation solvefor b,b^2+d^2=14bd ?

The solutions to the equation solvefor b,b^2+d^2=14bd are b=(7+4sqrt(3))d,b=(7-4sqrt(3))d

Find the zeros of solvefor b,b^2+d^2=14bd

The zeros of solvefor b,b^2+d^2=14bd are b=(7+4sqrt(3))d,b=(7-4sqrt(3))d

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solve for

b, b^{2} + d^{2} = 14 b d

b = (7 + 43) d, b = (7 - 43) d

Solution steps

b^{2} + d^{2} = 14 b d

Move

14 b d

to the left side

b^{2} + d^{2} - 14 b d = 0

Write in the standard form

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

b^{2} - 14 d b + d^{2} = 0

Solve with the quadratic formula

b_{1, 2} = \frac{- ( - 14 d ) \pm ( - 14 d ) ^{2} - 4 \cdot 1 \cdot d ^{2}}{2 \cdot 1}

Simplify

(- 14 d)^{2} - 4 \cdot 1 \cdot d^{2} : 83 d

b_{1, 2} = \frac{- ( - 14 d ) \pm 8 3 d}{2 \cdot 1}

Separate the solutions

b_{1} = \frac{- ( - 14 d ) + 8 3 d}{2 \cdot 1}, b_{2} = \frac{- ( - 14 d ) - 8 3 d}{2 \cdot 1}

b = \frac{- ( - 14 d ) + 8 3 d}{2 \cdot 1} : (7 + 43) d

b = \frac{- ( - 14 d ) - 8 3 d}{2 \cdot 1} : (7 - 43) d

The solutions to the quadratic equation are:

b = (7 + 43) d, b = (7 - 43) d

x, 36 x^{2} + 100 y^{2} - 72 x + 200 y + 3464 = 0

2 x^{2} = 15

2 x^{2} = 60

2 x^{2} = 49

7 x^{2} + 3 x - 3 = 0

What are the solutions to the equation solvefor b,b^2+d^2=14bd ?
The solutions to the equation solvefor b,b^2+d^2=14bd are b=(7+4sqrt(3))d,b=(7-4sqrt(3))d
Find the zeros of solvefor b,b^2+d^2=14bd
The zeros of solvefor b,b^2+d^2=14bd are b=(7+4sqrt(3))d,b=(7-4sqrt(3))d