4x+7+6x^2=8x^2-2x+10-3x^2

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Solution for 4x+7+6x^2=8x^2-2x+10-3x^2 equation:


Simplifying
4x + 7 + 6x2 = 8x2 + -2x + 10 + -3x2

Reorder the terms:
7 + 4x + 6x2 = 8x2 + -2x + 10 + -3x2

Reorder the terms:
7 + 4x + 6x2 = 10 + -2x + 8x2 + -3x2

Combine like terms: 8x2 + -3x2 = 5x2
7 + 4x + 6x2 = 10 + -2x + 5x2

Solving
7 + 4x + 6x2 = 10 + -2x + 5x2

Solving for variable 'x'.

Reorder the terms:
7 + -10 + 4x + 2x + 6x2 + -5x2 = 10 + -2x + 5x2 + -10 + 2x + -5x2

Combine like terms: 7 + -10 = -3
-3 + 4x + 2x + 6x2 + -5x2 = 10 + -2x + 5x2 + -10 + 2x + -5x2

Combine like terms: 4x + 2x = 6x
-3 + 6x + 6x2 + -5x2 = 10 + -2x + 5x2 + -10 + 2x + -5x2

Combine like terms: 6x2 + -5x2 = 1x2
-3 + 6x + 1x2 = 10 + -2x + 5x2 + -10 + 2x + -5x2

Reorder the terms:
-3 + 6x + 1x2 = 10 + -10 + -2x + 2x + 5x2 + -5x2

Combine like terms: 10 + -10 = 0
-3 + 6x + 1x2 = 0 + -2x + 2x + 5x2 + -5x2
-3 + 6x + 1x2 = -2x + 2x + 5x2 + -5x2

Combine like terms: -2x + 2x = 0
-3 + 6x + 1x2 = 0 + 5x2 + -5x2
-3 + 6x + 1x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
-3 + 6x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + 6x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + 6x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + 6x + x2 = 0 + 3
6x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
6x + x2 = 3

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 = 3 + 9

Reorder the terms:
9 + 6x + x2 = 3 + 9

Combine like terms: 3 + 9 = 12
9 + 6x + x2 = 12

Factor a perfect square on the left side:
(x + 3)(x + 3) = 12

Calculate the square root of the right side: 3.464101615

Break this problem into two subproblems by setting 
(x + 3) equal to 3.464101615 and -3.464101615.

Subproblem 1

x + 3 = 3.464101615 Simplifying x + 3 = 3.464101615 Reorder the terms: 3 + x = 3.464101615 Solving 3 + x = 3.464101615 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 = 3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.464101615 + -3 x = 3.464101615 + -3 Combine like terms: 3.464101615 + -3 = 0.464101615 x = 0.464101615 Simplifying x = 0.464101615

Subproblem 2

x + 3 = -3.464101615 Simplifying x + 3 = -3.464101615 Reorder the terms: 3 + x = -3.464101615 Solving 3 + x = -3.464101615 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 = -3.464101615 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.464101615 + -3 x = -3.464101615 + -3 Combine like terms: -3.464101615 + -3 = -6.464101615 x = -6.464101615 Simplifying x = -6.464101615

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.464101615, -6.464101615}

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