4t^2+21t-29=

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Solution for 4t^2+21t-29= equation:


Simplifying
4t2 + 21t + -29 = 0

Reorder the terms:
-29 + 21t + 4t2 = 0

Solving
-29 + 21t + 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'.
-7.25 + 5.25t + t2 = 0

Move the constant term to the right:

Add '7.25' to each side of the equation.
-7.25 + 5.25t + 7.25 + t2 = 0 + 7.25

Reorder the terms:
-7.25 + 7.25 + 5.25t + t2 = 0 + 7.25

Combine like terms: -7.25 + 7.25 = 0.00
0.00 + 5.25t + t2 = 0 + 7.25
5.25t + t2 = 0 + 7.25

Combine like terms: 0 + 7.25 = 7.25
5.25t + t2 = 7.25

The t term is 5.25t.  Take half its coefficient (2.625).
Square it (6.890625) and add it to both sides.

Add '6.890625' to each side of the equation.
5.25t + 6.890625 + t2 = 7.25 + 6.890625

Reorder the terms:
6.890625 + 5.25t + t2 = 7.25 + 6.890625

Combine like terms: 7.25 + 6.890625 = 14.140625
6.890625 + 5.25t + t2 = 14.140625

Factor a perfect square on the left side:
(t + 2.625)(t + 2.625) = 14.140625

Calculate the square root of the right side: 3.760402239

Break this problem into two subproblems by setting 
(t + 2.625) equal to 3.760402239 and -3.760402239.

Subproblem 1

t + 2.625 = 3.760402239 Simplifying t + 2.625 = 3.760402239 Reorder the terms: 2.625 + t = 3.760402239 Solving 2.625 + t = 3.760402239 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + t = 3.760402239 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + t = 3.760402239 + -2.625 t = 3.760402239 + -2.625 Combine like terms: 3.760402239 + -2.625 = 1.135402239 t = 1.135402239 Simplifying t = 1.135402239

Subproblem 2

t + 2.625 = -3.760402239 Simplifying t + 2.625 = -3.760402239 Reorder the terms: 2.625 + t = -3.760402239 Solving 2.625 + t = -3.760402239 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.625' to each side of the equation. 2.625 + -2.625 + t = -3.760402239 + -2.625 Combine like terms: 2.625 + -2.625 = 0.000 0.000 + t = -3.760402239 + -2.625 t = -3.760402239 + -2.625 Combine like terms: -3.760402239 + -2.625 = -6.385402239 t = -6.385402239 Simplifying t = -6.385402239

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.135402239, -6.385402239}

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