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

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


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

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

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

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

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

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

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

Solving
7 + -2x + -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'.
-7 + 2x + x2 = 0

Move the constant term to the right:

Add '7' to each side of the equation.
-7 + 2x + 7 + x2 = 0 + 7

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

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

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

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 7 + 1

Reorder the terms:
1 + 2x + x2 = 7 + 1

Combine like terms: 7 + 1 = 8
1 + 2x + x2 = 8

Factor a perfect square on the left side:
(x + 1)(x + 1) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + 1) equal to 2.828427125 and -2.828427125.

Subproblem 1

x + 1 = 2.828427125 Simplifying x + 1 = 2.828427125 Reorder the terms: 1 + x = 2.828427125 Solving 1 + x = 2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.828427125 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.828427125 + -1 x = 2.828427125 + -1 Combine like terms: 2.828427125 + -1 = 1.828427125 x = 1.828427125 Simplifying x = 1.828427125

Subproblem 2

x + 1 = -2.828427125 Simplifying x + 1 = -2.828427125 Reorder the terms: 1 + x = -2.828427125 Solving 1 + x = -2.828427125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.828427125 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.828427125 + -1 x = -2.828427125 + -1 Combine like terms: -2.828427125 + -1 = -3.828427125 x = -3.828427125 Simplifying x = -3.828427125

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.828427125, -3.828427125}

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