2x+5x^2=12

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Solution for 2x+5x^2=12 equation:


Simplifying
2x + 5x2 = 12

Solving
2x + 5x2 = 12

Solving for variable 'x'.

Reorder the terms:
-12 + 2x + 5x2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 2x + 5x2 = 0

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

Divide each side by '5'.
-2.4 + 0.4x + x2 = 0

Move the constant term to the right:

Add '2.4' to each side of the equation.
-2.4 + 0.4x + 2.4 + x2 = 0 + 2.4

Reorder the terms:
-2.4 + 2.4 + 0.4x + x2 = 0 + 2.4

Combine like terms: -2.4 + 2.4 = 0.0
0.0 + 0.4x + x2 = 0 + 2.4
0.4x + x2 = 0 + 2.4

Combine like terms: 0 + 2.4 = 2.4
0.4x + x2 = 2.4

The x term is 0.4x.  Take half its coefficient (0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
0.4x + 0.04 + x2 = 2.4 + 0.04

Reorder the terms:
0.04 + 0.4x + x2 = 2.4 + 0.04

Combine like terms: 2.4 + 0.04 = 2.44
0.04 + 0.4x + x2 = 2.44

Factor a perfect square on the left side:
(x + 0.2)(x + 0.2) = 2.44

Calculate the square root of the right side: 1.562049935

Break this problem into two subproblems by setting 
(x + 0.2) equal to 1.562049935 and -1.562049935.

Subproblem 1

x + 0.2 = 1.562049935 Simplifying x + 0.2 = 1.562049935 Reorder the terms: 0.2 + x = 1.562049935 Solving 0.2 + x = 1.562049935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = 1.562049935 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = 1.562049935 + -0.2 x = 1.562049935 + -0.2 Combine like terms: 1.562049935 + -0.2 = 1.362049935 x = 1.362049935 Simplifying x = 1.362049935

Subproblem 2

x + 0.2 = -1.562049935 Simplifying x + 0.2 = -1.562049935 Reorder the terms: 0.2 + x = -1.562049935 Solving 0.2 + x = -1.562049935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2' to each side of the equation. 0.2 + -0.2 + x = -1.562049935 + -0.2 Combine like terms: 0.2 + -0.2 = 0.0 0.0 + x = -1.562049935 + -0.2 x = -1.562049935 + -0.2 Combine like terms: -1.562049935 + -0.2 = -1.762049935 x = -1.762049935 Simplifying x = -1.762049935

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.362049935, -1.762049935}

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