-5a^2+16a=-54

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Solution for -5a^2+16a=-54 equation:


Simplifying
-5a2 + 16a = -54

Reorder the terms:
16a + -5a2 = -54

Solving
16a + -5a2 = -54

Solving for variable 'a'.

Reorder the terms:
54 + 16a + -5a2 = -54 + 54

Combine like terms: -54 + 54 = 0
54 + 16a + -5a2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-10.8 + -3.2a + a2 = 0

Move the constant term to the right:

Add '10.8' to each side of the equation.
-10.8 + -3.2a + 10.8 + a2 = 0 + 10.8

Reorder the terms:
-10.8 + 10.8 + -3.2a + a2 = 0 + 10.8

Combine like terms: -10.8 + 10.8 = 0.0
0.0 + -3.2a + a2 = 0 + 10.8
-3.2a + a2 = 0 + 10.8

Combine like terms: 0 + 10.8 = 10.8
-3.2a + a2 = 10.8

The a term is -3.2a.  Take half its coefficient (-1.6).
Square it (2.56) and add it to both sides.

Add '2.56' to each side of the equation.
-3.2a + 2.56 + a2 = 10.8 + 2.56

Reorder the terms:
2.56 + -3.2a + a2 = 10.8 + 2.56

Combine like terms: 10.8 + 2.56 = 13.36
2.56 + -3.2a + a2 = 13.36

Factor a perfect square on the left side:
(a + -1.6)(a + -1.6) = 13.36

Calculate the square root of the right side: 3.655133377

Break this problem into two subproblems by setting 
(a + -1.6) equal to 3.655133377 and -3.655133377.

Subproblem 1

a + -1.6 = 3.655133377 Simplifying a + -1.6 = 3.655133377 Reorder the terms: -1.6 + a = 3.655133377 Solving -1.6 + a = 3.655133377 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + a = 3.655133377 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + a = 3.655133377 + 1.6 a = 3.655133377 + 1.6 Combine like terms: 3.655133377 + 1.6 = 5.255133377 a = 5.255133377 Simplifying a = 5.255133377

Subproblem 2

a + -1.6 = -3.655133377 Simplifying a + -1.6 = -3.655133377 Reorder the terms: -1.6 + a = -3.655133377 Solving -1.6 + a = -3.655133377 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '1.6' to each side of the equation. -1.6 + 1.6 + a = -3.655133377 + 1.6 Combine like terms: -1.6 + 1.6 = 0.0 0.0 + a = -3.655133377 + 1.6 a = -3.655133377 + 1.6 Combine like terms: -3.655133377 + 1.6 = -2.055133377 a = -2.055133377 Simplifying a = -2.055133377

Solution

The solution to the problem is based on the solutions from the subproblems. a = {5.255133377, -2.055133377}

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