-7a^2-65a+8=0

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Solution for -7a^2-65a+8=0 equation:


Simplifying
-7a2 + -65a + 8 = 0

Reorder the terms:
8 + -65a + -7a2 = 0

Solving
8 + -65a + -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 + 9.285714286a + a2 = 0

Move the constant term to the right:

Add '1.142857143' to each side of the equation.
-1.142857143 + 9.285714286a + 1.142857143 + a2 = 0 + 1.142857143

Reorder the terms:
-1.142857143 + 1.142857143 + 9.285714286a + a2 = 0 + 1.142857143

Combine like terms: -1.142857143 + 1.142857143 = 0.000000000
0.000000000 + 9.285714286a + a2 = 0 + 1.142857143
9.285714286a + a2 = 0 + 1.142857143

Combine like terms: 0 + 1.142857143 = 1.142857143
9.285714286a + a2 = 1.142857143

The a term is 9.285714286a.  Take half its coefficient (4.642857143).
Square it (21.55612245) and add it to both sides.

Add '21.55612245' to each side of the equation.
9.285714286a + 21.55612245 + a2 = 1.142857143 + 21.55612245

Reorder the terms:
21.55612245 + 9.285714286a + a2 = 1.142857143 + 21.55612245

Combine like terms: 1.142857143 + 21.55612245 = 22.698979593
21.55612245 + 9.285714286a + a2 = 22.698979593

Factor a perfect square on the left side:
(a + 4.642857143)(a + 4.642857143) = 22.698979593

Calculate the square root of the right side: 4.764344613

Break this problem into two subproblems by setting 
(a + 4.642857143) equal to 4.764344613 and -4.764344613.

Subproblem 1

a + 4.642857143 = 4.764344613 Simplifying a + 4.642857143 = 4.764344613 Reorder the terms: 4.642857143 + a = 4.764344613 Solving 4.642857143 + a = 4.764344613 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.642857143' to each side of the equation. 4.642857143 + -4.642857143 + a = 4.764344613 + -4.642857143 Combine like terms: 4.642857143 + -4.642857143 = 0.000000000 0.000000000 + a = 4.764344613 + -4.642857143 a = 4.764344613 + -4.642857143 Combine like terms: 4.764344613 + -4.642857143 = 0.12148747 a = 0.12148747 Simplifying a = 0.12148747

Subproblem 2

a + 4.642857143 = -4.764344613 Simplifying a + 4.642857143 = -4.764344613 Reorder the terms: 4.642857143 + a = -4.764344613 Solving 4.642857143 + a = -4.764344613 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.642857143' to each side of the equation. 4.642857143 + -4.642857143 + a = -4.764344613 + -4.642857143 Combine like terms: 4.642857143 + -4.642857143 = 0.000000000 0.000000000 + a = -4.764344613 + -4.642857143 a = -4.764344613 + -4.642857143 Combine like terms: -4.764344613 + -4.642857143 = -9.407201756 a = -9.407201756 Simplifying a = -9.407201756

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.12148747, -9.407201756}

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