4t^2+2t-9=0

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Solution for 4t^2+2t-9=0 equation:


Simplifying
4t2 + 2t + -9 = 0

Reorder the terms:
-9 + 2t + 4t2 = 0

Solving
-9 + 2t + 4t2 = 0

Solving for variable 't'.

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

Divide each side by '4'.
-2.25 + 0.5t + t2 = 0

Move the constant term to the right:

Add '2.25' to each side of the equation.
-2.25 + 0.5t + 2.25 + t2 = 0 + 2.25

Reorder the terms:
-2.25 + 2.25 + 0.5t + t2 = 0 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + 0.5t + t2 = 0 + 2.25
0.5t + t2 = 0 + 2.25

Combine like terms: 0 + 2.25 = 2.25
0.5t + t2 = 2.25

The t term is 0.5t.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5t + 0.0625 + t2 = 2.25 + 0.0625

Reorder the terms:
0.0625 + 0.5t + t2 = 2.25 + 0.0625

Combine like terms: 2.25 + 0.0625 = 2.3125
0.0625 + 0.5t + t2 = 2.3125

Factor a perfect square on the left side:
(t + 0.25)(t + 0.25) = 2.3125

Calculate the square root of the right side: 1.520690633

Break this problem into two subproblems by setting 
(t + 0.25) equal to 1.520690633 and -1.520690633.

Subproblem 1

t + 0.25 = 1.520690633 Simplifying t + 0.25 = 1.520690633 Reorder the terms: 0.25 + t = 1.520690633 Solving 0.25 + t = 1.520690633 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + t = 1.520690633 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + t = 1.520690633 + -0.25 t = 1.520690633 + -0.25 Combine like terms: 1.520690633 + -0.25 = 1.270690633 t = 1.270690633 Simplifying t = 1.270690633

Subproblem 2

t + 0.25 = -1.520690633 Simplifying t + 0.25 = -1.520690633 Reorder the terms: 0.25 + t = -1.520690633 Solving 0.25 + t = -1.520690633 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + t = -1.520690633 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + t = -1.520690633 + -0.25 t = -1.520690633 + -0.25 Combine like terms: -1.520690633 + -0.25 = -1.770690633 t = -1.770690633 Simplifying t = -1.770690633

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.270690633, -1.770690633}

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