4x^2+3=-12x

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Solution for 4x^2+3=-12x equation:


Simplifying
4x2 + 3 = -12x

Reorder the terms:
3 + 4x2 = -12x

Solving
3 + 4x2 = -12x

Solving for variable 'x'.

Reorder the terms:
3 + 12x + 4x2 = -12x + 12x

Combine like terms: -12x + 12x = 0
3 + 12x + 4x2 = 0

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

Divide each side by '4'.
0.75 + 3x + x2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + 3x + -0.75 + x2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + 3x + x2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + 3x + x2 = 0 + -0.75
3x + x2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
3x + x2 = -0.75

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = -0.75 + 2.25

Reorder the terms:
2.25 + 3x + x2 = -0.75 + 2.25

Combine like terms: -0.75 + 2.25 = 1.5
2.25 + 3x + x2 = 1.5

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.224744871 and -1.224744871.

Subproblem 1

x + 1.5 = 1.224744871 Simplifying x + 1.5 = 1.224744871 Reorder the terms: 1.5 + x = 1.224744871 Solving 1.5 + x = 1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 1.224744871 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.224744871 + -1.5 x = 1.224744871 + -1.5 Combine like terms: 1.224744871 + -1.5 = -0.275255129 x = -0.275255129 Simplifying x = -0.275255129

Subproblem 2

x + 1.5 = -1.224744871 Simplifying x + 1.5 = -1.224744871 Reorder the terms: 1.5 + x = -1.224744871 Solving 1.5 + x = -1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -1.224744871 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.224744871 + -1.5 x = -1.224744871 + -1.5 Combine like terms: -1.224744871 + -1.5 = -2.724744871 x = -2.724744871 Simplifying x = -2.724744871

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.275255129, -2.724744871}

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