(3t^2-t+5)+(-7t^2+4t+6)=

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Solution for (3t^2-t+5)+(-7t^2+4t+6)= equation:


Simplifying
(3t2 + -1t + 5) + (-7t2 + 4t + 6) = 0

Reorder the terms:
(5 + -1t + 3t2) + (-7t2 + 4t + 6) = 0

Remove parenthesis around (5 + -1t + 3t2)
5 + -1t + 3t2 + (-7t2 + 4t + 6) = 0

Reorder the terms:
5 + -1t + 3t2 + (6 + 4t + -7t2) = 0

Remove parenthesis around (6 + 4t + -7t2)
5 + -1t + 3t2 + 6 + 4t + -7t2 = 0

Reorder the terms:
5 + 6 + -1t + 4t + 3t2 + -7t2 = 0

Combine like terms: 5 + 6 = 11
11 + -1t + 4t + 3t2 + -7t2 = 0

Combine like terms: -1t + 4t = 3t
11 + 3t + 3t2 + -7t2 = 0

Combine like terms: 3t2 + -7t2 = -4t2
11 + 3t + -4t2 = 0

Solving
11 + 3t + -4t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-2.75 + -0.75t + t2 = 0

Move the constant term to the right:

Add '2.75' to each side of the equation.
-2.75 + -0.75t + 2.75 + t2 = 0 + 2.75

Reorder the terms:
-2.75 + 2.75 + -0.75t + t2 = 0 + 2.75

Combine like terms: -2.75 + 2.75 = 0.00
0.00 + -0.75t + t2 = 0 + 2.75
-0.75t + t2 = 0 + 2.75

Combine like terms: 0 + 2.75 = 2.75
-0.75t + t2 = 2.75

The t term is -0.75t.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75t + 0.140625 + t2 = 2.75 + 0.140625

Reorder the terms:
0.140625 + -0.75t + t2 = 2.75 + 0.140625

Combine like terms: 2.75 + 0.140625 = 2.890625
0.140625 + -0.75t + t2 = 2.890625

Factor a perfect square on the left side:
(t + -0.375)(t + -0.375) = 2.890625

Calculate the square root of the right side: 1.700183814

Break this problem into two subproblems by setting 
(t + -0.375) equal to 1.700183814 and -1.700183814.

Subproblem 1

t + -0.375 = 1.700183814 Simplifying t + -0.375 = 1.700183814 Reorder the terms: -0.375 + t = 1.700183814 Solving -0.375 + t = 1.700183814 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + t = 1.700183814 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = 1.700183814 + 0.375 t = 1.700183814 + 0.375 Combine like terms: 1.700183814 + 0.375 = 2.075183814 t = 2.075183814 Simplifying t = 2.075183814

Subproblem 2

t + -0.375 = -1.700183814 Simplifying t + -0.375 = -1.700183814 Reorder the terms: -0.375 + t = -1.700183814 Solving -0.375 + t = -1.700183814 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + t = -1.700183814 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = -1.700183814 + 0.375 t = -1.700183814 + 0.375 Combine like terms: -1.700183814 + 0.375 = -1.325183814 t = -1.325183814 Simplifying t = -1.325183814

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.075183814, -1.325183814}

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