-a^2-7a+2=0

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


Simplifying
-1a2 + -7a + 2 = 0

Reorder the terms:
2 + -7a + -1a2 = 0

Solving
2 + -7a + -1a2 = 0

Solving for variable 'a'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-2 + 7a + a2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 7a + 2 + a2 = 0 + 2

Reorder the terms:
-2 + 2 + 7a + a2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + 7a + a2 = 0 + 2
7a + a2 = 0 + 2

Combine like terms: 0 + 2 = 2
7a + a2 = 2

The a term is 7a.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7a + 12.25 + a2 = 2 + 12.25

Reorder the terms:
12.25 + 7a + a2 = 2 + 12.25

Combine like terms: 2 + 12.25 = 14.25
12.25 + 7a + a2 = 14.25

Factor a perfect square on the left side:
(a + 3.5)(a + 3.5) = 14.25

Calculate the square root of the right side: 3.774917218

Break this problem into two subproblems by setting 
(a + 3.5) equal to 3.774917218 and -3.774917218.

Subproblem 1

a + 3.5 = 3.774917218 Simplifying a + 3.5 = 3.774917218 Reorder the terms: 3.5 + a = 3.774917218 Solving 3.5 + a = 3.774917218 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + a = 3.774917218 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + a = 3.774917218 + -3.5 a = 3.774917218 + -3.5 Combine like terms: 3.774917218 + -3.5 = 0.274917218 a = 0.274917218 Simplifying a = 0.274917218

Subproblem 2

a + 3.5 = -3.774917218 Simplifying a + 3.5 = -3.774917218 Reorder the terms: 3.5 + a = -3.774917218 Solving 3.5 + a = -3.774917218 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + a = -3.774917218 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + a = -3.774917218 + -3.5 a = -3.774917218 + -3.5 Combine like terms: -3.774917218 + -3.5 = -7.274917218 a = -7.274917218 Simplifying a = -7.274917218

Solution

The solution to the problem is based on the solutions from the subproblems. a = {0.274917218, -7.274917218}

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