4t^2-18t-21=0

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Solution for 4t^2-18t-21=0 equation:


Simplifying
4t2 + -18t + -21 = 0

Reorder the terms:
-21 + -18t + 4t2 = 0

Solving
-21 + -18t + 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'.
-5.25 + -4.5t + t2 = 0

Move the constant term to the right:

Add '5.25' to each side of the equation.
-5.25 + -4.5t + 5.25 + t2 = 0 + 5.25

Reorder the terms:
-5.25 + 5.25 + -4.5t + t2 = 0 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + -4.5t + t2 = 0 + 5.25
-4.5t + t2 = 0 + 5.25

Combine like terms: 0 + 5.25 = 5.25
-4.5t + t2 = 5.25

The t term is -4.5t.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5t + 5.0625 + t2 = 5.25 + 5.0625

Reorder the terms:
5.0625 + -4.5t + t2 = 5.25 + 5.0625

Combine like terms: 5.25 + 5.0625 = 10.3125
5.0625 + -4.5t + t2 = 10.3125

Factor a perfect square on the left side:
(t + -2.25)(t + -2.25) = 10.3125

Calculate the square root of the right side: 3.211308145

Break this problem into two subproblems by setting 
(t + -2.25) equal to 3.211308145 and -3.211308145.

Subproblem 1

t + -2.25 = 3.211308145 Simplifying t + -2.25 = 3.211308145 Reorder the terms: -2.25 + t = 3.211308145 Solving -2.25 + t = 3.211308145 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + t = 3.211308145 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = 3.211308145 + 2.25 t = 3.211308145 + 2.25 Combine like terms: 3.211308145 + 2.25 = 5.461308145 t = 5.461308145 Simplifying t = 5.461308145

Subproblem 2

t + -2.25 = -3.211308145 Simplifying t + -2.25 = -3.211308145 Reorder the terms: -2.25 + t = -3.211308145 Solving -2.25 + t = -3.211308145 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.25' to each side of the equation. -2.25 + 2.25 + t = -3.211308145 + 2.25 Combine like terms: -2.25 + 2.25 = 0.00 0.00 + t = -3.211308145 + 2.25 t = -3.211308145 + 2.25 Combine like terms: -3.211308145 + 2.25 = -0.961308145 t = -0.961308145 Simplifying t = -0.961308145

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.461308145, -0.961308145}

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