2t^2+4t-110=0

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Solution for 2t^2+4t-110=0 equation:


Simplifying
2t2 + 4t + -110 = 0

Reorder the terms:
-110 + 4t + 2t2 = 0

Solving
-110 + 4t + 2t2 = 0

Solving for variable 't'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-55 + 2t + t2) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(-55 + 2t + t2)' equal to zero and attempt to solve: Simplifying -55 + 2t + t2 = 0 Solving -55 + 2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '55' to each side of the equation. -55 + 2t + 55 + t2 = 0 + 55 Reorder the terms: -55 + 55 + 2t + t2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + 2t + t2 = 0 + 55 2t + t2 = 0 + 55 Combine like terms: 0 + 55 = 55 2t + t2 = 55 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = 55 + 1 Reorder the terms: 1 + 2t + t2 = 55 + 1 Combine like terms: 55 + 1 = 56 1 + 2t + t2 = 56 Factor a perfect square on the left side: (t + 1)(t + 1) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (t + 1) equal to 7.483314774 and -7.483314774.

Subproblem 1

t + 1 = 7.483314774 Simplifying t + 1 = 7.483314774 Reorder the terms: 1 + t = 7.483314774 Solving 1 + t = 7.483314774 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 7.483314774 + -1 Combine like terms: 1 + -1 = 0 0 + t = 7.483314774 + -1 t = 7.483314774 + -1 Combine like terms: 7.483314774 + -1 = 6.483314774 t = 6.483314774 Simplifying t = 6.483314774

Subproblem 2

t + 1 = -7.483314774 Simplifying t + 1 = -7.483314774 Reorder the terms: 1 + t = -7.483314774 Solving 1 + t = -7.483314774 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -7.483314774 + -1 Combine like terms: 1 + -1 = 0 0 + t = -7.483314774 + -1 t = -7.483314774 + -1 Combine like terms: -7.483314774 + -1 = -8.483314774 t = -8.483314774 Simplifying t = -8.483314774

Solution

The solution to the problem is based on the solutions from the subproblems. t = {6.483314774, -8.483314774}

Solution

t = {6.483314774, -8.483314774}

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