-14t+2t^2=3

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Solution for -14t+2t^2=3 equation:


Simplifying
-14t + 2t2 = 3

Solving
-14t + 2t2 = 3

Solving for variable 't'.

Reorder the terms:
-3 + -14t + 2t2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + -14t + 2t2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-1.5 + -7t + t2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + -7t + 1.5 + t2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + -7t + t2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + -7t + t2 = 0 + 1.5
-7t + t2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
-7t + t2 = 1.5

The t term is -7t.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7t + 12.25 + t2 = 1.5 + 12.25

Reorder the terms:
12.25 + -7t + t2 = 1.5 + 12.25

Combine like terms: 1.5 + 12.25 = 13.75
12.25 + -7t + t2 = 13.75

Factor a perfect square on the left side:
(t + -3.5)(t + -3.5) = 13.75

Calculate the square root of the right side: 3.708099244

Break this problem into two subproblems by setting 
(t + -3.5) equal to 3.708099244 and -3.708099244.

Subproblem 1

t + -3.5 = 3.708099244 Simplifying t + -3.5 = 3.708099244 Reorder the terms: -3.5 + t = 3.708099244 Solving -3.5 + t = 3.708099244 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = 3.708099244 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = 3.708099244 + 3.5 t = 3.708099244 + 3.5 Combine like terms: 3.708099244 + 3.5 = 7.208099244 t = 7.208099244 Simplifying t = 7.208099244

Subproblem 2

t + -3.5 = -3.708099244 Simplifying t + -3.5 = -3.708099244 Reorder the terms: -3.5 + t = -3.708099244 Solving -3.5 + t = -3.708099244 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + t = -3.708099244 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + t = -3.708099244 + 3.5 t = -3.708099244 + 3.5 Combine like terms: -3.708099244 + 3.5 = -0.208099244 t = -0.208099244 Simplifying t = -0.208099244

Solution

The solution to the problem is based on the solutions from the subproblems. t = {7.208099244, -0.208099244}

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