5a^2+42a+48=0

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Solution for 5a^2+42a+48=0 equation:


Simplifying
5a2 + 42a + 48 = 0

Reorder the terms:
48 + 42a + 5a2 = 0

Solving
48 + 42a + 5a2 = 0

Solving for variable 'a'.

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

Divide each side by '5'.
9.6 + 8.4a + a2 = 0

Move the constant term to the right:

Add '-9.6' to each side of the equation.
9.6 + 8.4a + -9.6 + a2 = 0 + -9.6

Reorder the terms:
9.6 + -9.6 + 8.4a + a2 = 0 + -9.6

Combine like terms: 9.6 + -9.6 = 0.0
0.0 + 8.4a + a2 = 0 + -9.6
8.4a + a2 = 0 + -9.6

Combine like terms: 0 + -9.6 = -9.6
8.4a + a2 = -9.6

The a term is 8.4a.  Take half its coefficient (4.2).
Square it (17.64) and add it to both sides.

Add '17.64' to each side of the equation.
8.4a + 17.64 + a2 = -9.6 + 17.64

Reorder the terms:
17.64 + 8.4a + a2 = -9.6 + 17.64

Combine like terms: -9.6 + 17.64 = 8.04
17.64 + 8.4a + a2 = 8.04

Factor a perfect square on the left side:
(a + 4.2)(a + 4.2) = 8.04

Calculate the square root of the right side: 2.835489376

Break this problem into two subproblems by setting 
(a + 4.2) equal to 2.835489376 and -2.835489376.

Subproblem 1

a + 4.2 = 2.835489376 Simplifying a + 4.2 = 2.835489376 Reorder the terms: 4.2 + a = 2.835489376 Solving 4.2 + a = 2.835489376 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.2' to each side of the equation. 4.2 + -4.2 + a = 2.835489376 + -4.2 Combine like terms: 4.2 + -4.2 = 0.0 0.0 + a = 2.835489376 + -4.2 a = 2.835489376 + -4.2 Combine like terms: 2.835489376 + -4.2 = -1.364510624 a = -1.364510624 Simplifying a = -1.364510624

Subproblem 2

a + 4.2 = -2.835489376 Simplifying a + 4.2 = -2.835489376 Reorder the terms: 4.2 + a = -2.835489376 Solving 4.2 + a = -2.835489376 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4.2' to each side of the equation. 4.2 + -4.2 + a = -2.835489376 + -4.2 Combine like terms: 4.2 + -4.2 = 0.0 0.0 + a = -2.835489376 + -4.2 a = -2.835489376 + -4.2 Combine like terms: -2.835489376 + -4.2 = -7.035489376 a = -7.035489376 Simplifying a = -7.035489376

Solution

The solution to the problem is based on the solutions from the subproblems. a = {-1.364510624, -7.035489376}

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