-5t^2+7t-0.6=0

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Solution for -5t^2+7t-0.6=0 equation:


Simplifying
-5t2 + 7t + -0.6 = 0

Reorder the terms:
-0.6 + 7t + -5t2 = 0

Solving
-0.6 + 7t + -5t2 = 0

Solving for variable 't'.

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
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 = 0.37
0.49 + -1.4t + t2 = 0.37

Factor a perfect square on the left side:
(t + -0.7)(t + -0.7) = 0.37

Calculate the square root of the right side: 0.608276253

Break this problem into two subproblems by setting 
(t + -0.7) equal to 0.608276253 and -0.608276253.

Subproblem 1

t + -0.7 = 0.608276253 Simplifying t + -0.7 = 0.608276253 Reorder the terms: -0.7 + t = 0.608276253 Solving -0.7 + t = 0.608276253 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 = 0.608276253 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + t = 0.608276253 + 0.7 t = 0.608276253 + 0.7 Combine like terms: 0.608276253 + 0.7 = 1.308276253 t = 1.308276253 Simplifying t = 1.308276253

Subproblem 2

t + -0.7 = -0.608276253 Simplifying t + -0.7 = -0.608276253 Reorder the terms: -0.7 + t = -0.608276253 Solving -0.7 + t = -0.608276253 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 = -0.608276253 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + t = -0.608276253 + 0.7 t = -0.608276253 + 0.7 Combine like terms: -0.608276253 + 0.7 = 0.091723747 t = 0.091723747 Simplifying t = 0.091723747

Solution

The solution to the problem is based on the solutions from the subproblems. t = {1.308276253, 0.091723747}

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