(64-4d^2)*(64-d^2)=1540

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Solution for (64-4d^2)*(64-d^2)=1540 equation:


Simplifying
(64 + -4d2)(64 + -1d2) = 1540

Multiply (64 + -4d2) * (64 + -1d2)
(64(64 + -1d2) + -4d2 * (64 + -1d2)) = 1540
((64 * 64 + -1d2 * 64) + -4d2 * (64 + -1d2)) = 1540
((4096 + -64d2) + -4d2 * (64 + -1d2)) = 1540
(4096 + -64d2 + (64 * -4d2 + -1d2 * -4d2)) = 1540
(4096 + -64d2 + (-256d2 + 4d4)) = 1540

Combine like terms: -64d2 + -256d2 = -320d2
(4096 + -320d2 + 4d4) = 1540

Solving
4096 + -320d2 + 4d4 = 1540

Solving for variable 'd'.

Reorder the terms:
4096 + -1540 + -320d2 + 4d4 = 1540 + -1540

Combine like terms: 4096 + -1540 = 2556
2556 + -320d2 + 4d4 = 1540 + -1540

Combine like terms: 1540 + -1540 = 0
2556 + -320d2 + 4d4 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(639 + -80d2 + d4) = 0

Factor a trinomial.
4((9 + -1d2)(71 + -1d2)) = 0

Factor a difference between two squares.
4(((3 + d)(3 + -1d))(71 + -1d2)) = 0

Ignore the factor 4.

Subproblem 1

Set the factor '(71 + -1d2)' equal to zero and attempt to solve: Simplifying 71 + -1d2 = 0 Solving 71 + -1d2 = 0 Move all terms containing d to the left, all other terms to the right. Add '-71' to each side of the equation. 71 + -71 + -1d2 = 0 + -71 Combine like terms: 71 + -71 = 0 0 + -1d2 = 0 + -71 -1d2 = 0 + -71 Combine like terms: 0 + -71 = -71 -1d2 = -71 Divide each side by '-1'. d2 = 71 Simplifying d2 = 71 Take the square root of each side: d = {-8.426149773, 8.426149773}

Subproblem 2

Set the factor '(3 + d)' equal to zero and attempt to solve: Simplifying 3 + d = 0 Solving 3 + d = 0 Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + d = 0 + -3 Combine like terms: 3 + -3 = 0 0 + d = 0 + -3 d = 0 + -3 Combine like terms: 0 + -3 = -3 d = -3 Simplifying d = -3

Subproblem 3

Set the factor '(3 + -1d)' equal to zero and attempt to solve: Simplifying 3 + -1d = 0 Solving 3 + -1d = 0 Move all terms containing d to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1d = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1d = 0 + -3 -1d = 0 + -3 Combine like terms: 0 + -3 = -3 -1d = -3 Divide each side by '-1'. d = 3 Simplifying d = 3

Solution

d = {-8.426149773, 8.426149773, -3, 3}

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