t^2-3t=38

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Solution for t^2-3t=38 equation:


Simplifying
t2 + -3t = 38

Reorder the terms:
-3t + t2 = 38

Solving
-3t + t2 = 38

Solving for variable 't'.

Reorder the terms:
-38 + -3t + t2 = 38 + -38

Combine like terms: 38 + -38 = 0
-38 + -3t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '38' to each side of the equation.
-38 + -3t + 38 + t2 = 0 + 38

Reorder the terms:
-38 + 38 + -3t + t2 = 0 + 38

Combine like terms: -38 + 38 = 0
0 + -3t + t2 = 0 + 38
-3t + t2 = 0 + 38

Combine like terms: 0 + 38 = 38
-3t + t2 = 38

The t term is -3t.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3t + 2.25 + t2 = 38 + 2.25

Reorder the terms:
2.25 + -3t + t2 = 38 + 2.25

Combine like terms: 38 + 2.25 = 40.25
2.25 + -3t + t2 = 40.25

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 40.25

Calculate the square root of the right side: 6.34428877

Break this problem into two subproblems by setting 
(t + -1.5) equal to 6.34428877 and -6.34428877.

Subproblem 1

t + -1.5 = 6.34428877 Simplifying t + -1.5 = 6.34428877 Reorder the terms: -1.5 + t = 6.34428877 Solving -1.5 + t = 6.34428877 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = 6.34428877 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 6.34428877 + 1.5 t = 6.34428877 + 1.5 Combine like terms: 6.34428877 + 1.5 = 7.84428877 t = 7.84428877 Simplifying t = 7.84428877

Subproblem 2

t + -1.5 = -6.34428877 Simplifying t + -1.5 = -6.34428877 Reorder the terms: -1.5 + t = -6.34428877 Solving -1.5 + t = -6.34428877 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + t = -6.34428877 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -6.34428877 + 1.5 t = -6.34428877 + 1.5 Combine like terms: -6.34428877 + 1.5 = -4.84428877 t = -4.84428877 Simplifying t = -4.84428877

Solution

The solution to the problem is based on the solutions from the subproblems. t = {7.84428877, -4.84428877}

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