(2x^2-5x-1)+(x^2-3x-7)=

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Solution for (2x^2-5x-1)+(x^2-3x-7)= equation:


Simplifying
(2x2 + -5x + -1) + (x2 + -3x + -7) = 0

Reorder the terms:
(-1 + -5x + 2x2) + (x2 + -3x + -7) = 0

Remove parenthesis around (-1 + -5x + 2x2)
-1 + -5x + 2x2 + (x2 + -3x + -7) = 0

Reorder the terms:
-1 + -5x + 2x2 + (-7 + -3x + x2) = 0

Remove parenthesis around (-7 + -3x + x2)
-1 + -5x + 2x2 + -7 + -3x + x2 = 0

Reorder the terms:
-1 + -7 + -5x + -3x + 2x2 + x2 = 0

Combine like terms: -1 + -7 = -8
-8 + -5x + -3x + 2x2 + x2 = 0

Combine like terms: -5x + -3x = -8x
-8 + -8x + 2x2 + x2 = 0

Combine like terms: 2x2 + x2 = 3x2
-8 + -8x + 3x2 = 0

Solving
-8 + -8x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-2.666666667 + -2.666666667x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -2.666666667x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -2.666666667x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -2.666666667x + x2 = 0 + 2.666666667
-2.666666667x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-2.666666667x + x2 = 2.666666667

The x term is -2.666666667x.  Take half its coefficient (-1.333333334).
Square it (1.777777780) and add it to both sides.

Add '1.777777780' to each side of the equation.
-2.666666667x + 1.777777780 + x2 = 2.666666667 + 1.777777780

Reorder the terms:
1.777777780 + -2.666666667x + x2 = 2.666666667 + 1.777777780

Combine like terms: 2.666666667 + 1.777777780 = 4.444444447
1.777777780 + -2.666666667x + x2 = 4.444444447

Factor a perfect square on the left side:
(x + -1.333333334)(x + -1.333333334) = 4.444444447

Calculate the square root of the right side: 2.108185107

Break this problem into two subproblems by setting 
(x + -1.333333334) equal to 2.108185107 and -2.108185107.

Subproblem 1

x + -1.333333334 = 2.108185107 Simplifying x + -1.333333334 = 2.108185107 Reorder the terms: -1.333333334 + x = 2.108185107 Solving -1.333333334 + x = 2.108185107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = 2.108185107 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = 2.108185107 + 1.333333334 x = 2.108185107 + 1.333333334 Combine like terms: 2.108185107 + 1.333333334 = 3.441518441 x = 3.441518441 Simplifying x = 3.441518441

Subproblem 2

x + -1.333333334 = -2.108185107 Simplifying x + -1.333333334 = -2.108185107 Reorder the terms: -1.333333334 + x = -2.108185107 Solving -1.333333334 + x = -2.108185107 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.333333334' to each side of the equation. -1.333333334 + 1.333333334 + x = -2.108185107 + 1.333333334 Combine like terms: -1.333333334 + 1.333333334 = 0.000000000 0.000000000 + x = -2.108185107 + 1.333333334 x = -2.108185107 + 1.333333334 Combine like terms: -2.108185107 + 1.333333334 = -0.774851773 x = -0.774851773 Simplifying x = -0.774851773

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.441518441, -0.774851773}

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