-t^2+35t-100=0

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Solution for -t^2+35t-100=0 equation:


Simplifying
-1t2 + 35t + -100 = 0

Reorder the terms:
-100 + 35t + -1t2 = 0

Solving
-100 + 35t + -1t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
100 + -35t + t2 = 0

Move the constant term to the right:

Add '-100' to each side of the equation.
100 + -35t + -100 + t2 = 0 + -100

Reorder the terms:
100 + -100 + -35t + t2 = 0 + -100

Combine like terms: 100 + -100 = 0
0 + -35t + t2 = 0 + -100
-35t + t2 = 0 + -100

Combine like terms: 0 + -100 = -100
-35t + t2 = -100

The t term is -35t.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35t + 306.25 + t2 = -100 + 306.25

Reorder the terms:
306.25 + -35t + t2 = -100 + 306.25

Combine like terms: -100 + 306.25 = 206.25
306.25 + -35t + t2 = 206.25

Factor a perfect square on the left side:
(t + -17.5)(t + -17.5) = 206.25

Calculate the square root of the right side: 14.361406616

Break this problem into two subproblems by setting 
(t + -17.5) equal to 14.361406616 and -14.361406616.

Subproblem 1

t + -17.5 = 14.361406616 Simplifying t + -17.5 = 14.361406616 Reorder the terms: -17.5 + t = 14.361406616 Solving -17.5 + t = 14.361406616 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + t = 14.361406616 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + t = 14.361406616 + 17.5 t = 14.361406616 + 17.5 Combine like terms: 14.361406616 + 17.5 = 31.861406616 t = 31.861406616 Simplifying t = 31.861406616

Subproblem 2

t + -17.5 = -14.361406616 Simplifying t + -17.5 = -14.361406616 Reorder the terms: -17.5 + t = -14.361406616 Solving -17.5 + t = -14.361406616 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + t = -14.361406616 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + t = -14.361406616 + 17.5 t = -14.361406616 + 17.5 Combine like terms: -14.361406616 + 17.5 = 3.138593384 t = 3.138593384 Simplifying t = 3.138593384

Solution

The solution to the problem is based on the solutions from the subproblems. t = {31.861406616, 3.138593384}

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