(7x^2-9)-(8+3x)-(2x^2-8x)=

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Solution for (7x^2-9)-(8+3x)-(2x^2-8x)= equation:


Simplifying
(7x2 + -9) + -1(8 + 3x) + -1(2x2 + -8x) = 0

Reorder the terms:
(-9 + 7x2) + -1(8 + 3x) + -1(2x2 + -8x) = 0

Remove parenthesis around (-9 + 7x2)
-9 + 7x2 + -1(8 + 3x) + -1(2x2 + -8x) = 0
-9 + 7x2 + (8 * -1 + 3x * -1) + -1(2x2 + -8x) = 0
-9 + 7x2 + (-8 + -3x) + -1(2x2 + -8x) = 0

Reorder the terms:
-9 + 7x2 + -8 + -3x + -1(-8x + 2x2) = 0
-9 + 7x2 + -8 + -3x + (-8x * -1 + 2x2 * -1) = 0
-9 + 7x2 + -8 + -3x + (8x + -2x2) = 0

Reorder the terms:
-9 + -8 + -3x + 8x + 7x2 + -2x2 = 0

Combine like terms: -9 + -8 = -17
-17 + -3x + 8x + 7x2 + -2x2 = 0

Combine like terms: -3x + 8x = 5x
-17 + 5x + 7x2 + -2x2 = 0

Combine like terms: 7x2 + -2x2 = 5x2
-17 + 5x + 5x2 = 0

Solving
-17 + 5x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-3.4 + x + x2 = 0

Move the constant term to the right:

Add '3.4' to each side of the equation.
-3.4 + x + 3.4 + x2 = 0 + 3.4

Reorder the terms:
-3.4 + 3.4 + x + x2 = 0 + 3.4

Combine like terms: -3.4 + 3.4 = 0.0
0.0 + x + x2 = 0 + 3.4
x + x2 = 0 + 3.4

Combine like terms: 0 + 3.4 = 3.4
x + x2 = 3.4

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 3.4 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 3.4 + 0.25

Combine like terms: 3.4 + 0.25 = 3.65
1.25 + x2 = 3.65

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 3.65

Calculate the square root of the right side: 1.910497317

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.910497317 and -1.910497317.

Subproblem 1

x + 0.5 = 1.910497317 Simplifying x + 0.5 = 1.910497317 Reorder the terms: 0.5 + x = 1.910497317 Solving 0.5 + x = 1.910497317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 1.910497317 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 1.910497317 + -0.5 x = 1.910497317 + -0.5 Combine like terms: 1.910497317 + -0.5 = 1.410497317 x = 1.410497317 Simplifying x = 1.410497317

Subproblem 2

x + 0.5 = -1.910497317 Simplifying x + 0.5 = -1.910497317 Reorder the terms: 0.5 + x = -1.910497317 Solving 0.5 + x = -1.910497317 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -1.910497317 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -1.910497317 + -0.5 x = -1.910497317 + -0.5 Combine like terms: -1.910497317 + -0.5 = -2.410497317 x = -2.410497317 Simplifying x = -2.410497317

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.410497317, -2.410497317}

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