7a^2+6a=20

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Solution for 7a^2+6a=20 equation:


Simplifying
7a2 + 6a = 20

Reorder the terms:
6a + 7a2 = 20

Solving
6a + 7a2 = 20

Solving for variable 'a'.

Reorder the terms:
-20 + 6a + 7a2 = 20 + -20

Combine like terms: 20 + -20 = 0
-20 + 6a + 7a2 = 0

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

Divide each side by '7'.
-2.857142857 + 0.8571428571a + a2 = 0

Move the constant term to the right:

Add '2.857142857' to each side of the equation.
-2.857142857 + 0.8571428571a + 2.857142857 + a2 = 0 + 2.857142857

Reorder the terms:
-2.857142857 + 2.857142857 + 0.8571428571a + a2 = 0 + 2.857142857

Combine like terms: -2.857142857 + 2.857142857 = 0.000000000
0.000000000 + 0.8571428571a + a2 = 0 + 2.857142857
0.8571428571a + a2 = 0 + 2.857142857

Combine like terms: 0 + 2.857142857 = 2.857142857
0.8571428571a + a2 = 2.857142857

The a term is 0.8571428571a.  Take half its coefficient (0.4285714286).
Square it (0.1836734694) and add it to both sides.

Add '0.1836734694' to each side of the equation.
0.8571428571a + 0.1836734694 + a2 = 2.857142857 + 0.1836734694

Reorder the terms:
0.1836734694 + 0.8571428571a + a2 = 2.857142857 + 0.1836734694

Combine like terms: 2.857142857 + 0.1836734694 = 3.0408163264
0.1836734694 + 0.8571428571a + a2 = 3.0408163264

Factor a perfect square on the left side:
(a + 0.4285714286)(a + 0.4285714286) = 3.0408163264

Calculate the square root of the right side: 1.743793659

Break this problem into two subproblems by setting 
(a + 0.4285714286) equal to 1.743793659 and -1.743793659.

Subproblem 1

a + 0.4285714286 = 1.743793659 Simplifying a + 0.4285714286 = 1.743793659 Reorder the terms: 0.4285714286 + a = 1.743793659 Solving 0.4285714286 + a = 1.743793659 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + a = 1.743793659 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + a = 1.743793659 + -0.4285714286 a = 1.743793659 + -0.4285714286 Combine like terms: 1.743793659 + -0.4285714286 = 1.3152222304 a = 1.3152222304 Simplifying a = 1.3152222304

Subproblem 2

a + 0.4285714286 = -1.743793659 Simplifying a + 0.4285714286 = -1.743793659 Reorder the terms: 0.4285714286 + a = -1.743793659 Solving 0.4285714286 + a = -1.743793659 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-0.4285714286' to each side of the equation. 0.4285714286 + -0.4285714286 + a = -1.743793659 + -0.4285714286 Combine like terms: 0.4285714286 + -0.4285714286 = 0.0000000000 0.0000000000 + a = -1.743793659 + -0.4285714286 a = -1.743793659 + -0.4285714286 Combine like terms: -1.743793659 + -0.4285714286 = -2.1723650876 a = -2.1723650876 Simplifying a = -2.1723650876

Solution

The solution to the problem is based on the solutions from the subproblems. a = {1.3152222304, -2.1723650876}

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