25t^2+35t-3=0

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Solution for 25t^2+35t-3=0 equation:


Simplifying
25t2 + 35t + -3 = 0

Reorder the terms:
-3 + 35t + 25t2 = 0

Solving
-3 + 35t + 25t2 = 0

Solving for variable 't'.

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

Divide each side by '25'.
-0.12 + 1.4t + t2 = 0

Move the constant term to the right:

Add '0.12' to each side of the equation.
-0.12 + 1.4t + 0.12 + t2 = 0 + 0.12

Reorder the terms:
-0.12 + 0.12 + 1.4t + t2 = 0 + 0.12

Combine like terms: -0.12 + 0.12 = 0.00
0.00 + 1.4t + t2 = 0 + 0.12
1.4t + t2 = 0 + 0.12

Combine like terms: 0 + 0.12 = 0.12
1.4t + t2 = 0.12

The t term is 1.4t.  Take half its coefficient (0.7).
Square it (0.49) and add it to both sides.

Add '0.49' to each side of the equation.
1.4t + 0.49 + t2 = 0.12 + 0.49

Reorder the terms:
0.49 + 1.4t + t2 = 0.12 + 0.49

Combine like terms: 0.12 + 0.49 = 0.61
0.49 + 1.4t + t2 = 0.61

Factor a perfect square on the left side:
(t + 0.7)(t + 0.7) = 0.61

Calculate the square root of the right side: 0.781024968

Break this problem into two subproblems by setting 
(t + 0.7) equal to 0.781024968 and -0.781024968.

Subproblem 1

t + 0.7 = 0.781024968 Simplifying t + 0.7 = 0.781024968 Reorder the terms: 0.7 + t = 0.781024968 Solving 0.7 + t = 0.781024968 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + t = 0.781024968 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + t = 0.781024968 + -0.7 t = 0.781024968 + -0.7 Combine like terms: 0.781024968 + -0.7 = 0.081024968 t = 0.081024968 Simplifying t = 0.081024968

Subproblem 2

t + 0.7 = -0.781024968 Simplifying t + 0.7 = -0.781024968 Reorder the terms: 0.7 + t = -0.781024968 Solving 0.7 + t = -0.781024968 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.7' to each side of the equation. 0.7 + -0.7 + t = -0.781024968 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + t = -0.781024968 + -0.7 t = -0.781024968 + -0.7 Combine like terms: -0.781024968 + -0.7 = -1.481024968 t = -1.481024968 Simplifying t = -1.481024968

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.081024968, -1.481024968}

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