t^2-24t+35=0

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Solution for t^2-24t+35=0 equation:


Simplifying
t2 + -24t + 35 = 0

Reorder the terms:
35 + -24t + t2 = 0

Solving
35 + -24t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-35' to each side of the equation.
35 + -24t + -35 + t2 = 0 + -35

Reorder the terms:
35 + -35 + -24t + t2 = 0 + -35

Combine like terms: 35 + -35 = 0
0 + -24t + t2 = 0 + -35
-24t + t2 = 0 + -35

Combine like terms: 0 + -35 = -35
-24t + t2 = -35

The t term is -24t.  Take half its coefficient (-12).
Square it (144) and add it to both sides.

Add '144' to each side of the equation.
-24t + 144 + t2 = -35 + 144

Reorder the terms:
144 + -24t + t2 = -35 + 144

Combine like terms: -35 + 144 = 109
144 + -24t + t2 = 109

Factor a perfect square on the left side:
(t + -12)(t + -12) = 109

Calculate the square root of the right side: 10.440306509

Break this problem into two subproblems by setting 
(t + -12) equal to 10.440306509 and -10.440306509.

Subproblem 1

t + -12 = 10.440306509 Simplifying t + -12 = 10.440306509 Reorder the terms: -12 + t = 10.440306509 Solving -12 + t = 10.440306509 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = 10.440306509 + 12 Combine like terms: -12 + 12 = 0 0 + t = 10.440306509 + 12 t = 10.440306509 + 12 Combine like terms: 10.440306509 + 12 = 22.440306509 t = 22.440306509 Simplifying t = 22.440306509

Subproblem 2

t + -12 = -10.440306509 Simplifying t + -12 = -10.440306509 Reorder the terms: -12 + t = -10.440306509 Solving -12 + t = -10.440306509 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + t = -10.440306509 + 12 Combine like terms: -12 + 12 = 0 0 + t = -10.440306509 + 12 t = -10.440306509 + 12 Combine like terms: -10.440306509 + 12 = 1.559693491 t = 1.559693491 Simplifying t = 1.559693491

Solution

The solution to the problem is based on the solutions from the subproblems. t = {22.440306509, 1.559693491}

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