15t^2+32t-70=0

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Solution for 15t^2+32t-70=0 equation: 


Simplifying
15t2 + 32t + -70 = 0

Reorder the terms:
-70 + 32t + 15t2 = 0

Solving
-70 + 32t + 15t2 = 0

Solving for variable 't'.

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

Divide each side by '15'.
-4.666666667 + 2.133333333t + t2 = 0

Move the constant term to the right:

Add '4.666666667' to each side of the equation.
-4.666666667 + 2.133333333t + 4.666666667 + t2 = 0 + 4.666666667

Reorder the terms:
-4.666666667 + 4.666666667 + 2.133333333t + t2 = 0 + 4.666666667

Combine like terms: -4.666666667 + 4.666666667 = 0.000000000
0.000000000 + 2.133333333t + t2 = 0 + 4.666666667
2.133333333t + t2 = 0 + 4.666666667

Combine like terms: 0 + 4.666666667 = 4.666666667
2.133333333t + t2 = 4.666666667

The t term is 2.133333333t.  Take half its coefficient (1.066666667).
Square it (1.137777778) and add it to both sides.

Add '1.137777778' to each side of the equation.
2.133333333t + 1.137777778 + t2 = 4.666666667 + 1.137777778

Reorder the terms:
1.137777778 + 2.133333333t + t2 = 4.666666667 + 1.137777778

Combine like terms: 4.666666667 + 1.137777778 = 5.804444445
1.137777778 + 2.133333333t + t2 = 5.804444445

Factor a perfect square on the left side:
(t + 1.066666667)(t + 1.066666667) = 5.804444445

Calculate the square root of the right side: 2.409241467

Break this problem into two subproblems by setting 
(t + 1.066666667) equal to 2.409241467 and -2.409241467.


Subproblem 1
t + 1.066666667 = 2.409241467

Simplifying
t + 1.066666667 = 2.409241467

Reorder the terms:
1.066666667 + t = 2.409241467

Solving
1.066666667 + t = 2.409241467

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-1.066666667' to each side of the equation.
1.066666667 + -1.066666667 + t = 2.409241467 + -1.066666667

Combine like terms: 1.066666667 + -1.066666667 = 0.000000000
0.000000000 + t = 2.409241467 + -1.066666667
t = 2.409241467 + -1.066666667

Combine like terms: 2.409241467 + -1.066666667 = 1.3425748
t = 1.3425748

Simplifying
t = 1.3425748


Subproblem 2
t + 1.066666667 = -2.409241467

Simplifying
t + 1.066666667 = -2.409241467

Reorder the terms:
1.066666667 + t = -2.409241467

Solving
1.066666667 + t = -2.409241467

Solving for variable 't'.

Move all terms containing t to the left, all other terms to the right.

Add '-1.066666667' to each side of the equation.
1.066666667 + -1.066666667 + t = -2.409241467 + -1.066666667

Combine like terms: 1.066666667 + -1.066666667 = 0.000000000
0.000000000 + t = -2.409241467 + -1.066666667
t = -2.409241467 + -1.066666667

Combine like terms: -2.409241467 + -1.066666667 = -3.475908134
t = -3.475908134

Simplifying
t = -3.475908134


Solution
The solution to the problem is based on the solutions
from the subproblems.
t = {1.3425748, -3.475908134}

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