1.75t^2-22t-96=0

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Solution for 1.75t^2-22t-96=0 equation:


Simplifying
1.75t2 + -22t + -96 = 0

Reorder the terms:
-96 + -22t + 1.75t2 = 0

Solving
-96 + -22t + 1.75t2 = 0

Solving for variable 't'.

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

Divide each side by '1.75'.
-54.85714286 + -12.57142857t + t2 = 0

Move the constant term to the right:

Add '54.85714286' to each side of the equation.
-54.85714286 + -12.57142857t + 54.85714286 + t2 = 0 + 54.85714286

Reorder the terms:
-54.85714286 + 54.85714286 + -12.57142857t + t2 = 0 + 54.85714286

Combine like terms: -54.85714286 + 54.85714286 = 0.00000000
0.00000000 + -12.57142857t + t2 = 0 + 54.85714286
-12.57142857t + t2 = 0 + 54.85714286

Combine like terms: 0 + 54.85714286 = 54.85714286
-12.57142857t + t2 = 54.85714286

The t term is -12.57142857t.  Take half its coefficient (-6.285714285).
Square it (39.51020407) and add it to both sides.

Add '39.51020407' to each side of the equation.
-12.57142857t + 39.51020407 + t2 = 54.85714286 + 39.51020407

Reorder the terms:
39.51020407 + -12.57142857t + t2 = 54.85714286 + 39.51020407

Combine like terms: 54.85714286 + 39.51020407 = 94.36734693
39.51020407 + -12.57142857t + t2 = 94.36734693

Factor a perfect square on the left side:
(t + -6.285714285)(t + -6.285714285) = 94.36734693

Calculate the square root of the right side: 9.714285714

Break this problem into two subproblems by setting 
(t + -6.285714285) equal to 9.714285714 and -9.714285714.

Subproblem 1

t + -6.285714285 = 9.714285714 Simplifying t + -6.285714285 = 9.714285714 Reorder the terms: -6.285714285 + t = 9.714285714 Solving -6.285714285 + t = 9.714285714 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.285714285' to each side of the equation. -6.285714285 + 6.285714285 + t = 9.714285714 + 6.285714285 Combine like terms: -6.285714285 + 6.285714285 = 0.000000000 0.000000000 + t = 9.714285714 + 6.285714285 t = 9.714285714 + 6.285714285 Combine like terms: 9.714285714 + 6.285714285 = 15.999999999 t = 15.999999999 Simplifying t = 15.999999999

Subproblem 2

t + -6.285714285 = -9.714285714 Simplifying t + -6.285714285 = -9.714285714 Reorder the terms: -6.285714285 + t = -9.714285714 Solving -6.285714285 + t = -9.714285714 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.285714285' to each side of the equation. -6.285714285 + 6.285714285 + t = -9.714285714 + 6.285714285 Combine like terms: -6.285714285 + 6.285714285 = 0.000000000 0.000000000 + t = -9.714285714 + 6.285714285 t = -9.714285714 + 6.285714285 Combine like terms: -9.714285714 + 6.285714285 = -3.428571429 t = -3.428571429 Simplifying t = -3.428571429

Solution

The solution to the problem is based on the solutions from the subproblems. t = {15.999999999, -3.428571429}

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