7x-5+2x^2=-3x

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


Simplifying
7x + -5 + 2x2 = -3x

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

Solving
-5 + 7x + 2x2 = -3x

Solving for variable 'x'.

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

Combine like terms: 7x + 3x = 10x
-5 + 10x + 2x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
-5 + 10x + 2x2 = 0

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

Divide each side by '2'.
-2.5 + 5x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 5x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 5x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 5x + x2 = 0 + 2.5
5x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
5x + x2 = 2.5

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 2.5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 2.5 + 6.25

Combine like terms: 2.5 + 6.25 = 8.75
6.25 + 5x + x2 = 8.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 8.75

Calculate the square root of the right side: 2.958039892

Break this problem into two subproblems by setting 
(x + 2.5) equal to 2.958039892 and -2.958039892.

Subproblem 1

x + 2.5 = 2.958039892 Simplifying x + 2.5 = 2.958039892 Reorder the terms: 2.5 + x = 2.958039892 Solving 2.5 + x = 2.958039892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.958039892 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.958039892 + -2.5 x = 2.958039892 + -2.5 Combine like terms: 2.958039892 + -2.5 = 0.458039892 x = 0.458039892 Simplifying x = 0.458039892

Subproblem 2

x + 2.5 = -2.958039892 Simplifying x + 2.5 = -2.958039892 Reorder the terms: 2.5 + x = -2.958039892 Solving 2.5 + x = -2.958039892 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.958039892 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.958039892 + -2.5 x = -2.958039892 + -2.5 Combine like terms: -2.958039892 + -2.5 = -5.458039892 x = -5.458039892 Simplifying x = -5.458039892

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.458039892, -5.458039892}

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