5t^2+7t=9

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Solution for 5t^2+7t=9 equation:


Simplifying
5t2 + 7t = 9

Reorder the terms:
7t + 5t2 = 9

Solving
7t + 5t2 = 9

Solving for variable 't'.

Reorder the terms:
-9 + 7t + 5t2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + 7t + 5t2 = 0

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

Divide each side by '5'.
-1.8 + 1.4t + t2 = 0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + 1.4t + 1.8 + t2 = 0 + 1.8

Reorder the terms:
-1.8 + 1.8 + 1.4t + t2 = 0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + 1.4t + t2 = 0 + 1.8
1.4t + t2 = 0 + 1.8

Combine like terms: 0 + 1.8 = 1.8
1.4t + t2 = 1.8

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 = 1.8 + 0.49

Reorder the terms:
0.49 + 1.4t + t2 = 1.8 + 0.49

Combine like terms: 1.8 + 0.49 = 2.29
0.49 + 1.4t + t2 = 2.29

Factor a perfect square on the left side:
(t + 0.7)(t + 0.7) = 2.29

Calculate the square root of the right side: 1.513274595

Break this problem into two subproblems by setting 
(t + 0.7) equal to 1.513274595 and -1.513274595.

Subproblem 1

t + 0.7 = 1.513274595 Simplifying t + 0.7 = 1.513274595 Reorder the terms: 0.7 + t = 1.513274595 Solving 0.7 + t = 1.513274595 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 = 1.513274595 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + t = 1.513274595 + -0.7 t = 1.513274595 + -0.7 Combine like terms: 1.513274595 + -0.7 = 0.813274595 t = 0.813274595 Simplifying t = 0.813274595

Subproblem 2

t + 0.7 = -1.513274595 Simplifying t + 0.7 = -1.513274595 Reorder the terms: 0.7 + t = -1.513274595 Solving 0.7 + t = -1.513274595 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 = -1.513274595 + -0.7 Combine like terms: 0.7 + -0.7 = 0.0 0.0 + t = -1.513274595 + -0.7 t = -1.513274595 + -0.7 Combine like terms: -1.513274595 + -0.7 = -2.213274595 t = -2.213274595 Simplifying t = -2.213274595

Solution

The solution to the problem is based on the solutions from the subproblems. t = {0.813274595, -2.213274595}

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