-256=-16t^2+32t

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Solution for -256=-16t^2+32t equation:


Simplifying
-256 = -16t2 + 32t

Reorder the terms:
-256 = 32t + -16t2

Solving
-256 = 32t + -16t2

Solving for variable 't'.

Reorder the terms:
-256 + -32t + 16t2 = 32t + -32t + -16t2 + 16t2

Combine like terms: 32t + -32t = 0
-256 + -32t + 16t2 = 0 + -16t2 + 16t2
-256 + -32t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-256 + -32t + 16t2 = 0

Factor out the Greatest Common Factor (GCF), '16'.
16(-16 + -2t + t2) = 0

Ignore the factor 16.

Subproblem 1

Set the factor '(-16 + -2t + t2)' equal to zero and attempt to solve: Simplifying -16 + -2t + t2 = 0 Solving -16 + -2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '16' to each side of the equation. -16 + -2t + 16 + t2 = 0 + 16 Reorder the terms: -16 + 16 + -2t + t2 = 0 + 16 Combine like terms: -16 + 16 = 0 0 + -2t + t2 = 0 + 16 -2t + t2 = 0 + 16 Combine like terms: 0 + 16 = 16 -2t + t2 = 16 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = 16 + 1 Reorder the terms: 1 + -2t + t2 = 16 + 1 Combine like terms: 16 + 1 = 17 1 + -2t + t2 = 17 Factor a perfect square on the left side: (t + -1)(t + -1) = 17 Calculate the square root of the right side: 4.123105626 Break this problem into two subproblems by setting (t + -1) equal to 4.123105626 and -4.123105626.

Subproblem 1

t + -1 = 4.123105626 Simplifying t + -1 = 4.123105626 Reorder the terms: -1 + t = 4.123105626 Solving -1 + t = 4.123105626 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = 4.123105626 + 1 Combine like terms: -1 + 1 = 0 0 + t = 4.123105626 + 1 t = 4.123105626 + 1 Combine like terms: 4.123105626 + 1 = 5.123105626 t = 5.123105626 Simplifying t = 5.123105626

Subproblem 2

t + -1 = -4.123105626 Simplifying t + -1 = -4.123105626 Reorder the terms: -1 + t = -4.123105626 Solving -1 + t = -4.123105626 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = -4.123105626 + 1 Combine like terms: -1 + 1 = 0 0 + t = -4.123105626 + 1 t = -4.123105626 + 1 Combine like terms: -4.123105626 + 1 = -3.123105626 t = -3.123105626 Simplifying t = -3.123105626

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.123105626, -3.123105626}

Solution

t = {5.123105626, -3.123105626}

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