0=-16t^2+160t+7

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Solution for 0=-16t^2+160t+7 equation:


Simplifying
0 = -16t2 + 160t + 7

Reorder the terms:
0 = 7 + 160t + -16t2

Solving
0 = 7 + 160t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -7 = -7
-7 + -160t + 16t2 = 7 + 160t + -16t2 + -7 + -160t + 16t2

Reorder the terms:
-7 + -160t + 16t2 = 7 + -7 + 160t + -160t + -16t2 + 16t2

Combine like terms: 7 + -7 = 0
-7 + -160t + 16t2 = 0 + 160t + -160t + -16t2 + 16t2
-7 + -160t + 16t2 = 160t + -160t + -16t2 + 16t2

Combine like terms: 160t + -160t = 0
-7 + -160t + 16t2 = 0 + -16t2 + 16t2
-7 + -160t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-7 + -160t + 16t2 = 0

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

Divide each side by '16'.
-0.4375 + -10t + t2 = 0

Move the constant term to the right:

Add '0.4375' to each side of the equation.
-0.4375 + -10t + 0.4375 + t2 = 0 + 0.4375

Reorder the terms:
-0.4375 + 0.4375 + -10t + t2 = 0 + 0.4375

Combine like terms: -0.4375 + 0.4375 = 0.0000
0.0000 + -10t + t2 = 0 + 0.4375
-10t + t2 = 0 + 0.4375

Combine like terms: 0 + 0.4375 = 0.4375
-10t + t2 = 0.4375

The t term is -10t.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10t + 25 + t2 = 0.4375 + 25

Reorder the terms:
25 + -10t + t2 = 0.4375 + 25

Combine like terms: 0.4375 + 25 = 25.4375
25 + -10t + t2 = 25.4375

Factor a perfect square on the left side:
(t + -5)(t + -5) = 25.4375

Calculate the square root of the right side: 5.04356025

Break this problem into two subproblems by setting 
(t + -5) equal to 5.04356025 and -5.04356025.

Subproblem 1

t + -5 = 5.04356025 Simplifying t + -5 = 5.04356025 Reorder the terms: -5 + t = 5.04356025 Solving -5 + t = 5.04356025 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = 5.04356025 + 5 Combine like terms: -5 + 5 = 0 0 + t = 5.04356025 + 5 t = 5.04356025 + 5 Combine like terms: 5.04356025 + 5 = 10.04356025 t = 10.04356025 Simplifying t = 10.04356025

Subproblem 2

t + -5 = -5.04356025 Simplifying t + -5 = -5.04356025 Reorder the terms: -5 + t = -5.04356025 Solving -5 + t = -5.04356025 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + t = -5.04356025 + 5 Combine like terms: -5 + 5 = 0 0 + t = -5.04356025 + 5 t = -5.04356025 + 5 Combine like terms: -5.04356025 + 5 = -0.04356025 t = -0.04356025 Simplifying t = -0.04356025

Solution

The solution to the problem is based on the solutions from the subproblems. t = {10.04356025, -0.04356025}

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