7a^2+5a-10=0

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Solution for 7a^2+5a-10=0 equation:


Simplifying
7a2 + 5a + -10 = 0

Reorder the terms:
-10 + 5a + 7a2 = 0

Solving
-10 + 5a + 7a2 = 0

Solving for variable 'a'.

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

Divide each side by '7'.
-1.428571429 + 0.7142857143a + a2 = 0

Move the constant term to the right:

Add '1.428571429' to each side of the equation.
-1.428571429 + 0.7142857143a + 1.428571429 + a2 = 0 + 1.428571429

Reorder the terms:
-1.428571429 + 1.428571429 + 0.7142857143a + a2 = 0 + 1.428571429

Combine like terms: -1.428571429 + 1.428571429 = 0.000000000
0.000000000 + 0.7142857143a + a2 = 0 + 1.428571429
0.7142857143a + a2 = 0 + 1.428571429

Combine like terms: 0 + 1.428571429 = 1.428571429
0.7142857143a + a2 = 1.428571429

The a term is 0.7142857143a.  Take half its coefficient (0.3571428572).
Square it (0.1275510204) and add it to both sides.

Add '0.1275510204' to each side of the equation.
0.7142857143a + 0.1275510204 + a2 = 1.428571429 + 0.1275510204

Reorder the terms:
0.1275510204 + 0.7142857143a + a2 = 1.428571429 + 0.1275510204

Combine like terms: 1.428571429 + 0.1275510204 = 1.5561224494
0.1275510204 + 0.7142857143a + a2 = 1.5561224494

Factor a perfect square on the left side:
(a + 0.3571428572)(a + 0.3571428572) = 1.5561224494

Calculate the square root of the right side: 1.247446371

Break this problem into two subproblems by setting 
(a + 0.3571428572) equal to 1.247446371 and -1.247446371.

Subproblem 1

a + 0.3571428572 = 1.247446371 Simplifying a + 0.3571428572 = 1.247446371 Reorder the terms: 0.3571428572 + a = 1.247446371 Solving 0.3571428572 + a = 1.247446371 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + a = 1.247446371 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + a = 1.247446371 + -0.3571428572 a = 1.247446371 + -0.3571428572 Combine like terms: 1.247446371 + -0.3571428572 = 0.8903035138 a = 0.8903035138 Simplifying a = 0.8903035138

Subproblem 2

a + 0.3571428572 = -1.247446371 Simplifying a + 0.3571428572 = -1.247446371 Reorder the terms: 0.3571428572 + a = -1.247446371 Solving 0.3571428572 + a = -1.247446371 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.3571428572' to each side of the equation. 0.3571428572 + -0.3571428572 + a = -1.247446371 + -0.3571428572 Combine like terms: 0.3571428572 + -0.3571428572 = 0.0000000000 0.0000000000 + a = -1.247446371 + -0.3571428572 a = -1.247446371 + -0.3571428572 Combine like terms: -1.247446371 + -0.3571428572 = -1.6045892282 a = -1.6045892282 Simplifying a = -1.6045892282

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.8903035138, -1.6045892282}

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