440=-16t^2-7t+470

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Solution for 440=-16t^2-7t+470 equation:


Simplifying
440 = -16t2 + -7t + 470

Reorder the terms:
440 = 470 + -7t + -16t2

Solving
440 = 470 + -7t + -16t2

Solving for variable 't'.

Combine like terms: 440 + -470 = -30
-30 + 7t + 16t2 = 470 + -7t + -16t2 + -470 + 7t + 16t2

Reorder the terms:
-30 + 7t + 16t2 = 470 + -470 + -7t + 7t + -16t2 + 16t2

Combine like terms: 470 + -470 = 0
-30 + 7t + 16t2 = 0 + -7t + 7t + -16t2 + 16t2
-30 + 7t + 16t2 = -7t + 7t + -16t2 + 16t2

Combine like terms: -7t + 7t = 0
-30 + 7t + 16t2 = 0 + -16t2 + 16t2
-30 + 7t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
-30 + 7t + 16t2 = 0

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

Divide each side by '16'.
-1.875 + 0.4375t + t2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + 0.4375t + 1.875 + t2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + 0.4375t + t2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + 0.4375t + t2 = 0 + 1.875
0.4375t + t2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
0.4375t + t2 = 1.875

The t term is 0.4375t.  Take half its coefficient (0.21875).
Square it (0.0478515625) and add it to both sides.

Add '0.0478515625' to each side of the equation.
0.4375t + 0.0478515625 + t2 = 1.875 + 0.0478515625

Reorder the terms:
0.0478515625 + 0.4375t + t2 = 1.875 + 0.0478515625

Combine like terms: 1.875 + 0.0478515625 = 1.9228515625
0.0478515625 + 0.4375t + t2 = 1.9228515625

Factor a perfect square on the left side:
(t + 0.21875)(t + 0.21875) = 1.9228515625

Calculate the square root of the right side: 1.386669233

Break this problem into two subproblems by setting 
(t + 0.21875) equal to 1.386669233 and -1.386669233.

Subproblem 1

t + 0.21875 = 1.386669233 Simplifying t + 0.21875 = 1.386669233 Reorder the terms: 0.21875 + t = 1.386669233 Solving 0.21875 + t = 1.386669233 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.21875' to each side of the equation. 0.21875 + -0.21875 + t = 1.386669233 + -0.21875 Combine like terms: 0.21875 + -0.21875 = 0.00000 0.00000 + t = 1.386669233 + -0.21875 t = 1.386669233 + -0.21875 Combine like terms: 1.386669233 + -0.21875 = 1.167919233 t = 1.167919233 Simplifying t = 1.167919233

Subproblem 2

t + 0.21875 = -1.386669233 Simplifying t + 0.21875 = -1.386669233 Reorder the terms: 0.21875 + t = -1.386669233 Solving 0.21875 + t = -1.386669233 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.21875' to each side of the equation. 0.21875 + -0.21875 + t = -1.386669233 + -0.21875 Combine like terms: 0.21875 + -0.21875 = 0.00000 0.00000 + t = -1.386669233 + -0.21875 t = -1.386669233 + -0.21875 Combine like terms: -1.386669233 + -0.21875 = -1.605419233 t = -1.605419233 Simplifying t = -1.605419233

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.167919233, -1.605419233}

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