t^2-3t-40=10

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Solution for t^2-3t-40=10 equation:


Simplifying
t2 + -3t + -40 = 10

Reorder the terms:
-40 + -3t + t2 = 10

Solving
-40 + -3t + t2 = 10

Solving for variable 't'.

Reorder the terms:
-40 + -10 + -3t + t2 = 10 + -10

Combine like terms: -40 + -10 = -50
-50 + -3t + t2 = 10 + -10

Combine like terms: 10 + -10 = 0
-50 + -3t + t2 = 0

Begin completing the square.

Move the constant term to the right:

Add '50' to each side of the equation.
-50 + -3t + 50 + t2 = 0 + 50

Reorder the terms:
-50 + 50 + -3t + t2 = 0 + 50

Combine like terms: -50 + 50 = 0
0 + -3t + t2 = 0 + 50
-3t + t2 = 0 + 50

Combine like terms: 0 + 50 = 50
-3t + t2 = 50

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 = 50 + 2.25

Reorder the terms:
2.25 + -3t + t2 = 50 + 2.25

Combine like terms: 50 + 2.25 = 52.25
2.25 + -3t + t2 = 52.25

Factor a perfect square on the left side:
(t + -1.5)(t + -1.5) = 52.25

Calculate the square root of the right side: 7.228416147

Break this problem into two subproblems by setting 
(t + -1.5) equal to 7.228416147 and -7.228416147.

Subproblem 1

t + -1.5 = 7.228416147 Simplifying t + -1.5 = 7.228416147 Reorder the terms: -1.5 + t = 7.228416147 Solving -1.5 + t = 7.228416147 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 = 7.228416147 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = 7.228416147 + 1.5 t = 7.228416147 + 1.5 Combine like terms: 7.228416147 + 1.5 = 8.728416147 t = 8.728416147 Simplifying t = 8.728416147

Subproblem 2

t + -1.5 = -7.228416147 Simplifying t + -1.5 = -7.228416147 Reorder the terms: -1.5 + t = -7.228416147 Solving -1.5 + t = -7.228416147 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 = -7.228416147 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + t = -7.228416147 + 1.5 t = -7.228416147 + 1.5 Combine like terms: -7.228416147 + 1.5 = -5.728416147 t = -5.728416147 Simplifying t = -5.728416147

Solution

The solution to the problem is based on the solutions from the subproblems. t = {8.728416147, -5.728416147}

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