(5x^2-3x+1)+(2x^2-4x-6)=

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Solution for (5x^2-3x+1)+(2x^2-4x-6)= equation:


Simplifying
(5x2 + -3x + 1) + (2x2 + -4x + -6) = 0

Reorder the terms:
(1 + -3x + 5x2) + (2x2 + -4x + -6) = 0

Remove parenthesis around (1 + -3x + 5x2)
1 + -3x + 5x2 + (2x2 + -4x + -6) = 0

Reorder the terms:
1 + -3x + 5x2 + (-6 + -4x + 2x2) = 0

Remove parenthesis around (-6 + -4x + 2x2)
1 + -3x + 5x2 + -6 + -4x + 2x2 = 0

Reorder the terms:
1 + -6 + -3x + -4x + 5x2 + 2x2 = 0

Combine like terms: 1 + -6 = -5
-5 + -3x + -4x + 5x2 + 2x2 = 0

Combine like terms: -3x + -4x = -7x
-5 + -7x + 5x2 + 2x2 = 0

Combine like terms: 5x2 + 2x2 = 7x2
-5 + -7x + 7x2 = 0

Solving
-5 + -7x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-0.7142857143 + -1x + x2 = 0

Move the constant term to the right:

Add '0.7142857143' to each side of the equation.
-0.7142857143 + -1x + 0.7142857143 + x2 = 0 + 0.7142857143

Reorder the terms:
-0.7142857143 + 0.7142857143 + -1x + x2 = 0 + 0.7142857143

Combine like terms: -0.7142857143 + 0.7142857143 = 0.0000000000
0.0000000000 + -1x + x2 = 0 + 0.7142857143
-1x + x2 = 0 + 0.7142857143

Combine like terms: 0 + 0.7142857143 = 0.7142857143
-1x + x2 = 0.7142857143

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 0.7142857143 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 0.7142857143 + 0.25

Combine like terms: 0.7142857143 + 0.25 = 0.9642857143
0.25 + -1x + x2 = 0.9642857143

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 0.9642857143

Calculate the square root of the right side: 0.981980506

Break this problem into two subproblems by setting 
(x + -0.5) equal to 0.981980506 and -0.981980506.

Subproblem 1

x + -0.5 = 0.981980506 Simplifying x + -0.5 = 0.981980506 Reorder the terms: -0.5 + x = 0.981980506 Solving -0.5 + x = 0.981980506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.981980506 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.981980506 + 0.5 x = 0.981980506 + 0.5 Combine like terms: 0.981980506 + 0.5 = 1.481980506 x = 1.481980506 Simplifying x = 1.481980506

Subproblem 2

x + -0.5 = -0.981980506 Simplifying x + -0.5 = -0.981980506 Reorder the terms: -0.5 + x = -0.981980506 Solving -0.5 + x = -0.981980506 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.981980506 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.981980506 + 0.5 x = -0.981980506 + 0.5 Combine like terms: -0.981980506 + 0.5 = -0.481980506 x = -0.481980506 Simplifying x = -0.481980506

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.481980506, -0.481980506}

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