15+13a=-a^2

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Solution for 15+13a=-a^2 equation:


Simplifying
15 + 13a = -1a2

Solving
15 + 13a = -1a2

Solving for variable 'a'.

Combine like terms: -1a2 + a2 = 0
15 + 13a + a2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-15' to each side of the equation.
15 + 13a + -15 + a2 = 0 + -15

Reorder the terms:
15 + -15 + 13a + a2 = 0 + -15

Combine like terms: 15 + -15 = 0
0 + 13a + a2 = 0 + -15
13a + a2 = 0 + -15

Combine like terms: 0 + -15 = -15
13a + a2 = -15

The a term is 13a.  Take half its coefficient (6.5).
Square it (42.25) and add it to both sides.

Add '42.25' to each side of the equation.
13a + 42.25 + a2 = -15 + 42.25

Reorder the terms:
42.25 + 13a + a2 = -15 + 42.25

Combine like terms: -15 + 42.25 = 27.25
42.25 + 13a + a2 = 27.25

Factor a perfect square on the left side:
(a + 6.5)(a + 6.5) = 27.25

Calculate the square root of the right side: 5.220153254

Break this problem into two subproblems by setting 
(a + 6.5) equal to 5.220153254 and -5.220153254.

Subproblem 1

a + 6.5 = 5.220153254 Simplifying a + 6.5 = 5.220153254 Reorder the terms: 6.5 + a = 5.220153254 Solving 6.5 + a = 5.220153254 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + a = 5.220153254 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + a = 5.220153254 + -6.5 a = 5.220153254 + -6.5 Combine like terms: 5.220153254 + -6.5 = -1.279846746 a = -1.279846746 Simplifying a = -1.279846746

Subproblem 2

a + 6.5 = -5.220153254 Simplifying a + 6.5 = -5.220153254 Reorder the terms: 6.5 + a = -5.220153254 Solving 6.5 + a = -5.220153254 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6.5' to each side of the equation. 6.5 + -6.5 + a = -5.220153254 + -6.5 Combine like terms: 6.5 + -6.5 = 0.0 0.0 + a = -5.220153254 + -6.5 a = -5.220153254 + -6.5 Combine like terms: -5.220153254 + -6.5 = -11.720153254 a = -11.720153254 Simplifying a = -11.720153254

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-1.279846746, -11.720153254}

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