7a^2+16a-8=0

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Solution for 7a^2+16a-8=0 equation:


Simplifying
7a2 + 16a + -8 = 0

Reorder the terms:
-8 + 16a + 7a2 = 0

Solving
-8 + 16a + 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'.
-1.142857143 + 2.285714286a + a2 = 0

Move the constant term to the right:

Add '1.142857143' to each side of the equation.
-1.142857143 + 2.285714286a + 1.142857143 + a2 = 0 + 1.142857143

Reorder the terms:
-1.142857143 + 1.142857143 + 2.285714286a + a2 = 0 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + 2.285714286a + a2 = 0 + 1.142857143
2.285714286a + a2 = 0 + 1.142857143

Combine like terms: 0 + 1.142857143 = 1.142857143
2.285714286a + a2 = 1.142857143

The a term is 2.285714286a.  Take half its coefficient (1.142857143).
Square it (1.306122449) and add it to both sides.

Add '1.306122449' to each side of the equation.
2.285714286a + 1.306122449 + a2 = 1.142857143 + 1.306122449

Reorder the terms:
1.306122449 + 2.285714286a + a2 = 1.142857143 + 1.306122449

Combine like terms: 1.142857143 + 1.306122449 = 2.448979592
1.306122449 + 2.285714286a + a2 = 2.448979592

Factor a perfect square on the left side:
(a + 1.142857143)(a + 1.142857143) = 2.448979592

Calculate the square root of the right side: 1.564921593

Break this problem into two subproblems by setting 
(a + 1.142857143) equal to 1.564921593 and -1.564921593.

Subproblem 1

a + 1.142857143 = 1.564921593 Simplifying a + 1.142857143 = 1.564921593 Reorder the terms: 1.142857143 + a = 1.564921593 Solving 1.142857143 + a = 1.564921593 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.142857143' to each side of the equation. 1.142857143 + -1.142857143 + a = 1.564921593 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + a = 1.564921593 + -1.142857143 a = 1.564921593 + -1.142857143 Combine like terms: 1.564921593 + -1.142857143 = 0.42206445 a = 0.42206445 Simplifying a = 0.42206445

Subproblem 2

a + 1.142857143 = -1.564921593 Simplifying a + 1.142857143 = -1.564921593 Reorder the terms: 1.142857143 + a = -1.564921593 Solving 1.142857143 + a = -1.564921593 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1.142857143' to each side of the equation. 1.142857143 + -1.142857143 + a = -1.564921593 + -1.142857143 Combine like terms: 1.142857143 + -1.142857143 = 0.000000000 0.000000000 + a = -1.564921593 + -1.142857143 a = -1.564921593 + -1.142857143 Combine like terms: -1.564921593 + -1.142857143 = -2.707778736 a = -2.707778736 Simplifying a = -2.707778736

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.42206445, -2.707778736}

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