t^2+18t=-61

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Solution for t^2+18t=-61 equation:


Simplifying
t2 + 18t = -61

Reorder the terms:
18t + t2 = -61

Solving
18t + t2 = -61

Solving for variable 't'.

Reorder the terms:
61 + 18t + t2 = -61 + 61

Combine like terms: -61 + 61 = 0
61 + 18t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-61' to each side of the equation.
61 + 18t + -61 + t2 = 0 + -61

Reorder the terms:
61 + -61 + 18t + t2 = 0 + -61

Combine like terms: 61 + -61 = 0
0 + 18t + t2 = 0 + -61
18t + t2 = 0 + -61

Combine like terms: 0 + -61 = -61
18t + t2 = -61

The t term is 18t.  Take half its coefficient (9).
Square it (81) and add it to both sides.

Add '81' to each side of the equation.
18t + 81 + t2 = -61 + 81

Reorder the terms:
81 + 18t + t2 = -61 + 81

Combine like terms: -61 + 81 = 20
81 + 18t + t2 = 20

Factor a perfect square on the left side:
(t + 9)(t + 9) = 20

Calculate the square root of the right side: 4.472135955

Break this problem into two subproblems by setting 
(t + 9) equal to 4.472135955 and -4.472135955.

Subproblem 1

t + 9 = 4.472135955 Simplifying t + 9 = 4.472135955 Reorder the terms: 9 + t = 4.472135955 Solving 9 + t = 4.472135955 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + t = 4.472135955 + -9 Combine like terms: 9 + -9 = 0 0 + t = 4.472135955 + -9 t = 4.472135955 + -9 Combine like terms: 4.472135955 + -9 = -4.527864045 t = -4.527864045 Simplifying t = -4.527864045

Subproblem 2

t + 9 = -4.472135955 Simplifying t + 9 = -4.472135955 Reorder the terms: 9 + t = -4.472135955 Solving 9 + t = -4.472135955 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + t = -4.472135955 + -9 Combine like terms: 9 + -9 = 0 0 + t = -4.472135955 + -9 t = -4.472135955 + -9 Combine like terms: -4.472135955 + -9 = -13.472135955 t = -13.472135955 Simplifying t = -13.472135955

Solution

The solution to the problem is based on the solutions from the subproblems. t = {-4.527864045, -13.472135955}

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