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Simplifying
(4c + -7d)(4c + 7d) = 0
Multiply (4c + -7d) * (4c + 7d)
(4c * (4c + 7d) + -7d * (4c + 7d)) = 0
((4c * 4c + 7d * 4c) + -7d * (4c + 7d)) = 0
Reorder the terms:
((28cd + 16c2) + -7d * (4c + 7d)) = 0
((28cd + 16c2) + -7d * (4c + 7d)) = 0
(28cd + 16c2 + (4c * -7d + 7d * -7d)) = 0
(28cd + 16c2 + (-28cd + -49d2)) = 0
Reorder the terms:
(28cd + -28cd + 16c2 + -49d2) = 0
Combine like terms: 28cd + -28cd = 0
(0 + 16c2 + -49d2) = 0
(16c2 + -49d2) = 0
Solving
16c2 + -49d2 = 0
Solving for variable 'c'.
Move all terms containing c to the left, all other terms to the right.
Add '49d2' to each side of the equation.
16c2 + -49d2 + 49d2 = 0 + 49d2
Combine like terms: -49d2 + 49d2 = 0
16c2 + 0 = 0 + 49d2
16c2 = 0 + 49d2
Remove the zero:
16c2 = 49d2
Divide each side by '16'.
c2 = 3.0625d2
Simplifying
c2 = 3.0625d2
Take the square root of each side:
c = {-1.75d, 1.75d}
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