1t^2-4t-6=

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Solution for 1t^2-4t-6= equation:


Simplifying
1t2 + -4t + -6 = 0

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

Solving
-6 + -4t + 1t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -4t + 6 + t2 = 0 + 6

Reorder the terms:
-6 + 6 + -4t + t2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -4t + t2 = 0 + 6
-4t + t2 = 0 + 6

Combine like terms: 0 + 6 = 6
-4t + t2 = 6

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = 6 + 4

Reorder the terms:
4 + -4t + t2 = 6 + 4

Combine like terms: 6 + 4 = 10
4 + -4t + t2 = 10

Factor a perfect square on the left side:
(t + -2)(t + -2) = 10

Calculate the square root of the right side: 3.16227766

Break this problem into two subproblems by setting 
(t + -2) equal to 3.16227766 and -3.16227766.

Subproblem 1

t + -2 = 3.16227766 Simplifying t + -2 = 3.16227766 Reorder the terms: -2 + t = 3.16227766 Solving -2 + t = 3.16227766 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 3.16227766 + 2 Combine like terms: -2 + 2 = 0 0 + t = 3.16227766 + 2 t = 3.16227766 + 2 Combine like terms: 3.16227766 + 2 = 5.16227766 t = 5.16227766 Simplifying t = 5.16227766

Subproblem 2

t + -2 = -3.16227766 Simplifying t + -2 = -3.16227766 Reorder the terms: -2 + t = -3.16227766 Solving -2 + t = -3.16227766 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -3.16227766 + 2 Combine like terms: -2 + 2 = 0 0 + t = -3.16227766 + 2 t = -3.16227766 + 2 Combine like terms: -3.16227766 + 2 = -1.16227766 t = -1.16227766 Simplifying t = -1.16227766

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.16227766, -1.16227766}

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