7a^2+13a=10

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Solution for 7a^2+13a=10 equation:


Simplifying
7a2 + 13a = 10

Reorder the terms:
13a + 7a2 = 10

Solving
13a + 7a2 = 10

Solving for variable 'a'.

Reorder the terms:
-10 + 13a + 7a2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 13a + 7a2 = 0

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

Divide each side by '7'.
-1.428571429 + 1.857142857a + a2 = 0

Move the constant term to the right:

Add '1.428571429' to each side of the equation.
-1.428571429 + 1.857142857a + 1.428571429 + a2 = 0 + 1.428571429

Reorder the terms:
-1.428571429 + 1.428571429 + 1.857142857a + a2 = 0 + 1.428571429

Combine like terms: -1.428571429 + 1.428571429 = 0.000000000
0.000000000 + 1.857142857a + a2 = 0 + 1.428571429
1.857142857a + a2 = 0 + 1.428571429

Combine like terms: 0 + 1.428571429 = 1.428571429
1.857142857a + a2 = 1.428571429

The a term is 1.857142857a.  Take half its coefficient (0.9285714285).
Square it (0.8622448978) and add it to both sides.

Add '0.8622448978' to each side of the equation.
1.857142857a + 0.8622448978 + a2 = 1.428571429 + 0.8622448978

Reorder the terms:
0.8622448978 + 1.857142857a + a2 = 1.428571429 + 0.8622448978

Combine like terms: 1.428571429 + 0.8622448978 = 2.2908163268
0.8622448978 + 1.857142857a + a2 = 2.2908163268

Factor a perfect square on the left side:
(a + 0.9285714285)(a + 0.9285714285) = 2.2908163268

Calculate the square root of the right side: 1.513544293

Break this problem into two subproblems by setting 
(a + 0.9285714285) equal to 1.513544293 and -1.513544293.

Subproblem 1

a + 0.9285714285 = 1.513544293 Simplifying a + 0.9285714285 = 1.513544293 Reorder the terms: 0.9285714285 + a = 1.513544293 Solving 0.9285714285 + a = 1.513544293 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + a = 1.513544293 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + a = 1.513544293 + -0.9285714285 a = 1.513544293 + -0.9285714285 Combine like terms: 1.513544293 + -0.9285714285 = 0.5849728645 a = 0.5849728645 Simplifying a = 0.5849728645

Subproblem 2

a + 0.9285714285 = -1.513544293 Simplifying a + 0.9285714285 = -1.513544293 Reorder the terms: 0.9285714285 + a = -1.513544293 Solving 0.9285714285 + a = -1.513544293 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + a = -1.513544293 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + a = -1.513544293 + -0.9285714285 a = -1.513544293 + -0.9285714285 Combine like terms: -1.513544293 + -0.9285714285 = -2.4421157215 a = -2.4421157215 Simplifying a = -2.4421157215

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.5849728645, -2.4421157215}

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