0=-16t^2+2.4t+0.075

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Solution for 0=-16t^2+2.4t+0.075 equation:


Simplifying
0 = -16t2 + 2.4t + 0.075

Reorder the terms:
0 = 0.075 + 2.4t + -16t2

Solving
0 = 0.075 + 2.4t + -16t2

Solving for variable 't'.

Combine like terms: 0 + -0.075 = -0.075
-0.075 + -2.4t + 16t2 = 0.075 + 2.4t + -16t2 + -0.075 + -2.4t + 16t2

Reorder the terms:
-0.075 + -2.4t + 16t2 = 0.075 + -0.075 + 2.4t + -2.4t + -16t2 + 16t2

Combine like terms: 0.075 + -0.075 = 0.000
-0.075 + -2.4t + 16t2 = 0.000 + 2.4t + -2.4t + -16t2 + 16t2
-0.075 + -2.4t + 16t2 = 2.4t + -2.4t + -16t2 + 16t2

Combine like terms: 2.4t + -2.4t = 0.0
-0.075 + -2.4t + 16t2 = 0.0 + -16t2 + 16t2
-0.075 + -2.4t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-0.075 + -2.4t + 16t2 = 0

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

Divide each side by '16'.
-0.0046875 + -0.15t + t2 = 0

Move the constant term to the right:

Add '0.0046875' to each side of the equation.
-0.0046875 + -0.15t + 0.0046875 + t2 = 0 + 0.0046875

Reorder the terms:
-0.0046875 + 0.0046875 + -0.15t + t2 = 0 + 0.0046875

Combine like terms: -0.0046875 + 0.0046875 = 0.0000000
0.0000000 + -0.15t + t2 = 0 + 0.0046875
-0.15t + t2 = 0 + 0.0046875

Combine like terms: 0 + 0.0046875 = 0.0046875
-0.15t + t2 = 0.0046875

The t term is -0.15t.  Take half its coefficient (-0.075).
Square it (0.005625) and add it to both sides.

Add '0.005625' to each side of the equation.
-0.15t + 0.005625 + t2 = 0.0046875 + 0.005625

Reorder the terms:
0.005625 + -0.15t + t2 = 0.0046875 + 0.005625

Combine like terms: 0.0046875 + 0.005625 = 0.0103125
0.005625 + -0.15t + t2 = 0.0103125

Factor a perfect square on the left side:
(t + -0.075)(t + -0.075) = 0.0103125

Calculate the square root of the right side: 0.10155048

Break this problem into two subproblems by setting 
(t + -0.075) equal to 0.10155048 and -0.10155048.

Subproblem 1

t + -0.075 = 0.10155048 Simplifying t + -0.075 = 0.10155048 Reorder the terms: -0.075 + t = 0.10155048 Solving -0.075 + t = 0.10155048 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.075' to each side of the equation. -0.075 + 0.075 + t = 0.10155048 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + t = 0.10155048 + 0.075 t = 0.10155048 + 0.075 Combine like terms: 0.10155048 + 0.075 = 0.17655048 t = 0.17655048 Simplifying t = 0.17655048

Subproblem 2

t + -0.075 = -0.10155048 Simplifying t + -0.075 = -0.10155048 Reorder the terms: -0.075 + t = -0.10155048 Solving -0.075 + t = -0.10155048 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.075' to each side of the equation. -0.075 + 0.075 + t = -0.10155048 + 0.075 Combine like terms: -0.075 + 0.075 = 0.000 0.000 + t = -0.10155048 + 0.075 t = -0.10155048 + 0.075 Combine like terms: -0.10155048 + 0.075 = -0.02655048 t = -0.02655048 Simplifying t = -0.02655048

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.17655048, -0.02655048}

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