3t^2+8=t^2-3t-12

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Solution for 3t^2+8=t^2-3t-12 equation:


Simplifying
3t2 + 8 = t2 + -3t + -12

Reorder the terms:
8 + 3t2 = t2 + -3t + -12

Reorder the terms:
8 + 3t2 = -12 + -3t + t2

Solving
8 + 3t2 = -12 + -3t + t2

Solving for variable 't'.

Reorder the terms:
8 + 12 + 3t + 3t2 + -1t2 = -12 + -3t + t2 + 12 + 3t + -1t2

Combine like terms: 8 + 12 = 20
20 + 3t + 3t2 + -1t2 = -12 + -3t + t2 + 12 + 3t + -1t2

Combine like terms: 3t2 + -1t2 = 2t2
20 + 3t + 2t2 = -12 + -3t + t2 + 12 + 3t + -1t2

Reorder the terms:
20 + 3t + 2t2 = -12 + 12 + -3t + 3t + t2 + -1t2

Combine like terms: -12 + 12 = 0
20 + 3t + 2t2 = 0 + -3t + 3t + t2 + -1t2
20 + 3t + 2t2 = -3t + 3t + t2 + -1t2

Combine like terms: -3t + 3t = 0
20 + 3t + 2t2 = 0 + t2 + -1t2
20 + 3t + 2t2 = t2 + -1t2

Combine like terms: t2 + -1t2 = 0
20 + 3t + 2t2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
10 + 1.5t + t2 = 0

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 1.5t + -10 + t2 = 0 + -10

Reorder the terms:
10 + -10 + 1.5t + t2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 1.5t + t2 = 0 + -10
1.5t + t2 = 0 + -10

Combine like terms: 0 + -10 = -10
1.5t + t2 = -10

The t term is 1.5t.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5t + 0.5625 + t2 = -10 + 0.5625

Reorder the terms:
0.5625 + 1.5t + t2 = -10 + 0.5625

Combine like terms: -10 + 0.5625 = -9.4375
0.5625 + 1.5t + t2 = -9.4375

Factor a perfect square on the left side:
(t + 0.75)(t + 0.75) = -9.4375

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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