t^2+t=2.4

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Solution for t^2+t=2.4 equation:


Simplifying
t2 + t = 2.4

Reorder the terms:
t + t2 = 2.4

Solving
t + t2 = 2.4

Solving for variable 't'.

Reorder the terms:
-2.4 + t + t2 = 2.4 + -2.4

Combine like terms: 2.4 + -2.4 = 0.0
-2.4 + t + t2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + t + 2.4 + t2 = 0.0 + 2.4

Reorder the terms:
-2.4 + 2.4 + t + t2 = 0.0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + t + t2 = 0.0 + 2.4
t + t2 = 0.0 + 2.4

Combine like terms: 0.0 + 2.4 = 2.4
t + t2 = 2.4

The t term is t.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
t + 0.25 + t2 = 2.4 + 0.25

Reorder the terms:
0.25 + t + t2 = 2.4 + 0.25

Combine like terms: 2.4 + 0.25 = 2.65
0.25 + t + t2 = 2.65

Factor a perfect square on the left side:
(t + 0.5)(t + 0.5) = 2.65

Calculate the square root of the right side: 1.62788206

Break this problem into two subproblems by setting 
(t + 0.5) equal to 1.62788206 and -1.62788206.

Subproblem 1

t + 0.5 = 1.62788206 Simplifying t + 0.5 = 1.62788206 Reorder the terms: 0.5 + t = 1.62788206 Solving 0.5 + t = 1.62788206 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 1.62788206 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 1.62788206 + -0.5 t = 1.62788206 + -0.5 Combine like terms: 1.62788206 + -0.5 = 1.12788206 t = 1.12788206 Simplifying t = 1.12788206

Subproblem 2

t + 0.5 = -1.62788206 Simplifying t + 0.5 = -1.62788206 Reorder the terms: 0.5 + t = -1.62788206 Solving 0.5 + t = -1.62788206 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -1.62788206 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -1.62788206 + -0.5 t = -1.62788206 + -0.5 Combine like terms: -1.62788206 + -0.5 = -2.12788206 t = -2.12788206 Simplifying t = -2.12788206

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.12788206, -2.12788206}

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