5x^2=-12x-6

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Solution for 5x^2=-12x-6 equation:


Simplifying
5x2 = -12x + -6

Reorder the terms:
5x2 = -6 + -12x

Solving
5x2 = -6 + -12x

Solving for variable 'x'.

Reorder the terms:
6 + 12x + 5x2 = -6 + -12x + 6 + 12x

Reorder the terms:
6 + 12x + 5x2 = -6 + 6 + -12x + 12x

Combine like terms: -6 + 6 = 0
6 + 12x + 5x2 = 0 + -12x + 12x
6 + 12x + 5x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
6 + 12x + 5x2 = 0

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

Divide each side by '5'.
1.2 + 2.4x + x2 = 0

Move the constant term to the right:

Add '-1.2' to each side of the equation.
1.2 + 2.4x + -1.2 + x2 = 0 + -1.2

Reorder the terms:
1.2 + -1.2 + 2.4x + x2 = 0 + -1.2

Combine like terms: 1.2 + -1.2 = 0.0
0.0 + 2.4x + x2 = 0 + -1.2
2.4x + x2 = 0 + -1.2

Combine like terms: 0 + -1.2 = -1.2
2.4x + x2 = -1.2

The x term is 2.4x.  Take half its coefficient (1.2).
Square it (1.44) and add it to both sides.

Add '1.44' to each side of the equation.
2.4x + 1.44 + x2 = -1.2 + 1.44

Reorder the terms:
1.44 + 2.4x + x2 = -1.2 + 1.44

Combine like terms: -1.2 + 1.44 = 0.24
1.44 + 2.4x + x2 = 0.24

Factor a perfect square on the left side:
(x + 1.2)(x + 1.2) = 0.24

Calculate the square root of the right side: 0.489897949

Break this problem into two subproblems by setting 
(x + 1.2) equal to 0.489897949 and -0.489897949.

Subproblem 1

x + 1.2 = 0.489897949 Simplifying x + 1.2 = 0.489897949 Reorder the terms: 1.2 + x = 0.489897949 Solving 1.2 + x = 0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = 0.489897949 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 0.489897949 + -1.2 x = 0.489897949 + -1.2 Combine like terms: 0.489897949 + -1.2 = -0.710102051 x = -0.710102051 Simplifying x = -0.710102051

Subproblem 2

x + 1.2 = -0.489897949 Simplifying x + 1.2 = -0.489897949 Reorder the terms: 1.2 + x = -0.489897949 Solving 1.2 + x = -0.489897949 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.2' to each side of the equation. 1.2 + -1.2 + x = -0.489897949 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -0.489897949 + -1.2 x = -0.489897949 + -1.2 Combine like terms: -0.489897949 + -1.2 = -1.689897949 x = -1.689897949 Simplifying x = -1.689897949

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.710102051, -1.689897949}

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