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

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


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

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

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

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

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

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

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

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

Solving
-4 + 6x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
4 + -6x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + -6x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + -6x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -6x + x2 = 0 + -4
-6x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
-6x + x2 = -4

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = -4 + 9

Reorder the terms:
9 + -6x + x2 = -4 + 9

Combine like terms: -4 + 9 = 5
9 + -6x + x2 = 5

Factor a perfect square on the left side:
(x + -3)(x + -3) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -3) equal to 2.236067978 and -2.236067978.

Subproblem 1

x + -3 = 2.236067978 Simplifying x + -3 = 2.236067978 Reorder the terms: -3 + x = 2.236067978 Solving -3 + x = 2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.236067978 + 3 x = 2.236067978 + 3 Combine like terms: 2.236067978 + 3 = 5.236067978 x = 5.236067978 Simplifying x = 5.236067978

Subproblem 2

x + -3 = -2.236067978 Simplifying x + -3 = -2.236067978 Reorder the terms: -3 + x = -2.236067978 Solving -3 + x = -2.236067978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.236067978 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.236067978 + 3 x = -2.236067978 + 3 Combine like terms: -2.236067978 + 3 = 0.763932022 x = 0.763932022 Simplifying x = 0.763932022

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.236067978, 0.763932022}

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