-.2t^2+1.6t+.64=-.64

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Solution for -.2t^2+1.6t+.64=-.64 equation:


Simplifying
-0.2t2 + 1.6t + 0.64 = -0.64

Reorder the terms:
0.64 + 1.6t + -0.2t2 = -0.64

Solving
0.64 + 1.6t + -0.2t2 = -0.64

Solving for variable 't'.

Reorder the terms:
0.64 + 0.64 + 1.6t + -0.2t2 = -0.64 + 0.64

Combine like terms: 0.64 + 0.64 = 1.28
1.28 + 1.6t + -0.2t2 = -0.64 + 0.64

Combine like terms: -0.64 + 0.64 = 0.00
1.28 + 1.6t + -0.2t2 = 0.00

Begin completing the square.  Divide all terms by
-0.2 the coefficient of the squared term: 

Divide each side by '-0.2'.
-6.4 + -8t + t2 = 0.0

Move the constant term to the right:

Add '6.4' to each side of the equation.
-6.4 + -8t + 6.4 + t2 = 0.0 + 6.4

Reorder the terms:
-6.4 + 6.4 + -8t + t2 = 0.0 + 6.4

Combine like terms: -6.4 + 6.4 = 0.0
0.0 + -8t + t2 = 0.0 + 6.4
-8t + t2 = 0.0 + 6.4

Combine like terms: 0.0 + 6.4 = 6.4
-8t + t2 = 6.4

The t term is -8t.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8t + 16 + t2 = 6.4 + 16

Reorder the terms:
16 + -8t + t2 = 6.4 + 16

Combine like terms: 6.4 + 16 = 22.4
16 + -8t + t2 = 22.4

Factor a perfect square on the left side:
(t + -4)(t + -4) = 22.4

Calculate the square root of the right side: 4.732863826

Break this problem into two subproblems by setting 
(t + -4) equal to 4.732863826 and -4.732863826.

Subproblem 1

t + -4 = 4.732863826 Simplifying t + -4 = 4.732863826 Reorder the terms: -4 + t = 4.732863826 Solving -4 + t = 4.732863826 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 4.732863826 + 4 Combine like terms: -4 + 4 = 0 0 + t = 4.732863826 + 4 t = 4.732863826 + 4 Combine like terms: 4.732863826 + 4 = 8.732863826 t = 8.732863826 Simplifying t = 8.732863826

Subproblem 2

t + -4 = -4.732863826 Simplifying t + -4 = -4.732863826 Reorder the terms: -4 + t = -4.732863826 Solving -4 + t = -4.732863826 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -4.732863826 + 4 Combine like terms: -4 + 4 = 0 0 + t = -4.732863826 + 4 t = -4.732863826 + 4 Combine like terms: -4.732863826 + 4 = -0.732863826 t = -0.732863826 Simplifying t = -0.732863826

Solution

The solution to the problem is based on the solutions from the subproblems. t = {8.732863826, -0.732863826}

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