40=-16t^2+62t+5

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Solution for 40=-16t^2+62t+5 equation:


Simplifying
40 = -16t2 + 62t + 5

Reorder the terms:
40 = 5 + 62t + -16t2

Solving
40 = 5 + 62t + -16t2

Solving for variable 't'.

Combine like terms: 40 + -5 = 35
35 + -62t + 16t2 = 5 + 62t + -16t2 + -5 + -62t + 16t2

Reorder the terms:
35 + -62t + 16t2 = 5 + -5 + 62t + -62t + -16t2 + 16t2

Combine like terms: 5 + -5 = 0
35 + -62t + 16t2 = 0 + 62t + -62t + -16t2 + 16t2
35 + -62t + 16t2 = 62t + -62t + -16t2 + 16t2

Combine like terms: 62t + -62t = 0
35 + -62t + 16t2 = 0 + -16t2 + 16t2
35 + -62t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
35 + -62t + 16t2 = 0

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

Divide each side by '16'.
2.1875 + -3.875t + t2 = 0

Move the constant term to the right:

Add '-2.1875' to each side of the equation.
2.1875 + -3.875t + -2.1875 + t2 = 0 + -2.1875

Reorder the terms:
2.1875 + -2.1875 + -3.875t + t2 = 0 + -2.1875

Combine like terms: 2.1875 + -2.1875 = 0.0000
0.0000 + -3.875t + t2 = 0 + -2.1875
-3.875t + t2 = 0 + -2.1875

Combine like terms: 0 + -2.1875 = -2.1875
-3.875t + t2 = -2.1875

The t term is -3.875t.  Take half its coefficient (-1.9375).
Square it (3.75390625) and add it to both sides.

Add '3.75390625' to each side of the equation.
-3.875t + 3.75390625 + t2 = -2.1875 + 3.75390625

Reorder the terms:
3.75390625 + -3.875t + t2 = -2.1875 + 3.75390625

Combine like terms: -2.1875 + 3.75390625 = 1.56640625
3.75390625 + -3.875t + t2 = 1.56640625

Factor a perfect square on the left side:
(t + -1.9375)(t + -1.9375) = 1.56640625

Calculate the square root of the right side: 1.251561525

Break this problem into two subproblems by setting 
(t + -1.9375) equal to 1.251561525 and -1.251561525.

Subproblem 1

t + -1.9375 = 1.251561525 Simplifying t + -1.9375 = 1.251561525 Reorder the terms: -1.9375 + t = 1.251561525 Solving -1.9375 + t = 1.251561525 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + t = 1.251561525 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + t = 1.251561525 + 1.9375 t = 1.251561525 + 1.9375 Combine like terms: 1.251561525 + 1.9375 = 3.189061525 t = 3.189061525 Simplifying t = 3.189061525

Subproblem 2

t + -1.9375 = -1.251561525 Simplifying t + -1.9375 = -1.251561525 Reorder the terms: -1.9375 + t = -1.251561525 Solving -1.9375 + t = -1.251561525 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.9375' to each side of the equation. -1.9375 + 1.9375 + t = -1.251561525 + 1.9375 Combine like terms: -1.9375 + 1.9375 = 0.0000 0.0000 + t = -1.251561525 + 1.9375 t = -1.251561525 + 1.9375 Combine like terms: -1.251561525 + 1.9375 = 0.685938475 t = 0.685938475 Simplifying t = 0.685938475

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3.189061525, 0.685938475}

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