t^2+9t-18=0

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Solution for t^2+9t-18=0 equation:


Simplifying
t2 + 9t + -18 = 0

Reorder the terms:
-18 + 9t + t2 = 0

Solving
-18 + 9t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '18' to each side of the equation.
-18 + 9t + 18 + t2 = 0 + 18

Reorder the terms:
-18 + 18 + 9t + t2 = 0 + 18

Combine like terms: -18 + 18 = 0
0 + 9t + t2 = 0 + 18
9t + t2 = 0 + 18

Combine like terms: 0 + 18 = 18
9t + t2 = 18

The t term is 9t.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9t + 20.25 + t2 = 18 + 20.25

Reorder the terms:
20.25 + 9t + t2 = 18 + 20.25

Combine like terms: 18 + 20.25 = 38.25
20.25 + 9t + t2 = 38.25

Factor a perfect square on the left side:
(t + 4.5)(t + 4.5) = 38.25

Calculate the square root of the right side: 6.184658438

Break this problem into two subproblems by setting 
(t + 4.5) equal to 6.184658438 and -6.184658438.

Subproblem 1

t + 4.5 = 6.184658438 Simplifying t + 4.5 = 6.184658438 Reorder the terms: 4.5 + t = 6.184658438 Solving 4.5 + t = 6.184658438 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + t = 6.184658438 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + t = 6.184658438 + -4.5 t = 6.184658438 + -4.5 Combine like terms: 6.184658438 + -4.5 = 1.684658438 t = 1.684658438 Simplifying t = 1.684658438

Subproblem 2

t + 4.5 = -6.184658438 Simplifying t + 4.5 = -6.184658438 Reorder the terms: 4.5 + t = -6.184658438 Solving 4.5 + t = -6.184658438 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + t = -6.184658438 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + t = -6.184658438 + -4.5 t = -6.184658438 + -4.5 Combine like terms: -6.184658438 + -4.5 = -10.684658438 t = -10.684658438 Simplifying t = -10.684658438

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.684658438, -10.684658438}

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