-5x^2-12x+4=0

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Solution for -5x^2-12x+4=0 equation:


Simplifying
-5x2 + -12x + 4 = 0

Reorder the terms:
4 + -12x + -5x2 = 0

Solving
4 + -12x + -5x2 = 0

Solving for variable 'x'.

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

Divide each side by '-5'.
-0.8 + 2.4x + x2 = 0

Move the constant term to the right:

Add '0.8' to each side of the equation.
-0.8 + 2.4x + 0.8 + x2 = 0 + 0.8

Reorder the terms:
-0.8 + 0.8 + 2.4x + x2 = 0 + 0.8

Combine like terms: -0.8 + 0.8 = 0.0
0.0 + 2.4x + x2 = 0 + 0.8
2.4x + x2 = 0 + 0.8

Combine like terms: 0 + 0.8 = 0.8
2.4x + x2 = 0.8

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 = 0.8 + 1.44

Reorder the terms:
1.44 + 2.4x + x2 = 0.8 + 1.44

Combine like terms: 0.8 + 1.44 = 2.24
1.44 + 2.4x + x2 = 2.24

Factor a perfect square on the left side:
(x + 1.2)(x + 1.2) = 2.24

Calculate the square root of the right side: 1.496662955

Break this problem into two subproblems by setting 
(x + 1.2) equal to 1.496662955 and -1.496662955.

Subproblem 1

x + 1.2 = 1.496662955 Simplifying x + 1.2 = 1.496662955 Reorder the terms: 1.2 + x = 1.496662955 Solving 1.2 + x = 1.496662955 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 = 1.496662955 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = 1.496662955 + -1.2 x = 1.496662955 + -1.2 Combine like terms: 1.496662955 + -1.2 = 0.296662955 x = 0.296662955 Simplifying x = 0.296662955

Subproblem 2

x + 1.2 = -1.496662955 Simplifying x + 1.2 = -1.496662955 Reorder the terms: 1.2 + x = -1.496662955 Solving 1.2 + x = -1.496662955 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 = -1.496662955 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + x = -1.496662955 + -1.2 x = -1.496662955 + -1.2 Combine like terms: -1.496662955 + -1.2 = -2.696662955 x = -2.696662955 Simplifying x = -2.696662955

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.296662955, -2.696662955}

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