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

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


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

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

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

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

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

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

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

Solving
-1 + 3x + -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'.
1 + -3x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -3x + -1 + x2 = 0 + -1

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

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

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

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = -1 + 2.25

Reorder the terms:
2.25 + -3x + x2 = -1 + 2.25

Combine like terms: -1 + 2.25 = 1.25
2.25 + -3x + x2 = 1.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + -1.5) equal to 1.118033989 and -1.118033989.

Subproblem 1

x + -1.5 = 1.118033989 Simplifying x + -1.5 = 1.118033989 Reorder the terms: -1.5 + x = 1.118033989 Solving -1.5 + x = 1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 1.118033989 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 1.118033989 + 1.5 x = 1.118033989 + 1.5 Combine like terms: 1.118033989 + 1.5 = 2.618033989 x = 2.618033989 Simplifying x = 2.618033989

Subproblem 2

x + -1.5 = -1.118033989 Simplifying x + -1.5 = -1.118033989 Reorder the terms: -1.5 + x = -1.118033989 Solving -1.5 + x = -1.118033989 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -1.118033989 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -1.118033989 + 1.5 x = -1.118033989 + 1.5 Combine like terms: -1.118033989 + 1.5 = 0.381966011 x = 0.381966011 Simplifying x = 0.381966011

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.618033989, 0.381966011}

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