t^2+31t+145=0

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Solution for t^2+31t+145=0 equation:


Simplifying
t2 + 31t + 145 = 0

Reorder the terms:
145 + 31t + t2 = 0

Solving
145 + 31t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '-145' to each side of the equation.
145 + 31t + -145 + t2 = 0 + -145

Reorder the terms:
145 + -145 + 31t + t2 = 0 + -145

Combine like terms: 145 + -145 = 0
0 + 31t + t2 = 0 + -145
31t + t2 = 0 + -145

Combine like terms: 0 + -145 = -145
31t + t2 = -145

The t term is 31t.  Take half its coefficient (15.5).
Square it (240.25) and add it to both sides.

Add '240.25' to each side of the equation.
31t + 240.25 + t2 = -145 + 240.25

Reorder the terms:
240.25 + 31t + t2 = -145 + 240.25

Combine like terms: -145 + 240.25 = 95.25
240.25 + 31t + t2 = 95.25

Factor a perfect square on the left side:
(t + 15.5)(t + 15.5) = 95.25

Calculate the square root of the right side: 9.759610648

Break this problem into two subproblems by setting 
(t + 15.5) equal to 9.759610648 and -9.759610648.

Subproblem 1

t + 15.5 = 9.759610648 Simplifying t + 15.5 = 9.759610648 Reorder the terms: 15.5 + t = 9.759610648 Solving 15.5 + t = 9.759610648 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + t = 9.759610648 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + t = 9.759610648 + -15.5 t = 9.759610648 + -15.5 Combine like terms: 9.759610648 + -15.5 = -5.740389352 t = -5.740389352 Simplifying t = -5.740389352

Subproblem 2

t + 15.5 = -9.759610648 Simplifying t + 15.5 = -9.759610648 Reorder the terms: 15.5 + t = -9.759610648 Solving 15.5 + t = -9.759610648 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-15.5' to each side of the equation. 15.5 + -15.5 + t = -9.759610648 + -15.5 Combine like terms: 15.5 + -15.5 = 0.0 0.0 + t = -9.759610648 + -15.5 t = -9.759610648 + -15.5 Combine like terms: -9.759610648 + -15.5 = -25.259610648 t = -25.259610648 Simplifying t = -25.259610648

Solution

The solution to the problem is based on the solutions from the subproblems. t = {-5.740389352, -25.259610648}

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