2x^2-20x=7x^2-3x-8

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Solution for 2x^2-20x=7x^2-3x-8 equation:


Simplifying
2x2 + -20x = 7x2 + -3x + -8

Reorder the terms:
-20x + 2x2 = 7x2 + -3x + -8

Reorder the terms:
-20x + 2x2 = -8 + -3x + 7x2

Solving
-20x + 2x2 = -8 + -3x + 7x2

Solving for variable 'x'.

Reorder the terms:
8 + -20x + 3x + 2x2 + -7x2 = -8 + -3x + 7x2 + 8 + 3x + -7x2

Combine like terms: -20x + 3x = -17x
8 + -17x + 2x2 + -7x2 = -8 + -3x + 7x2 + 8 + 3x + -7x2

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

Reorder the terms:
8 + -17x + -5x2 = -8 + 8 + -3x + 3x + 7x2 + -7x2

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

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

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

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

Divide each side by '-5'.
-1.6 + 3.4x + x2 = 0

Move the constant term to the right:

Add '1.6' to each side of the equation.
-1.6 + 3.4x + 1.6 + x2 = 0 + 1.6

Reorder the terms:
-1.6 + 1.6 + 3.4x + x2 = 0 + 1.6

Combine like terms: -1.6 + 1.6 = 0.0
0.0 + 3.4x + x2 = 0 + 1.6
3.4x + x2 = 0 + 1.6

Combine like terms: 0 + 1.6 = 1.6
3.4x + x2 = 1.6

The x term is 3.4x.  Take half its coefficient (1.7).
Square it (2.89) and add it to both sides.

Add '2.89' to each side of the equation.
3.4x + 2.89 + x2 = 1.6 + 2.89

Reorder the terms:
2.89 + 3.4x + x2 = 1.6 + 2.89

Combine like terms: 1.6 + 2.89 = 4.49
2.89 + 3.4x + x2 = 4.49

Factor a perfect square on the left side:
(x + 1.7)(x + 1.7) = 4.49

Calculate the square root of the right side: 2.11896201

Break this problem into two subproblems by setting 
(x + 1.7) equal to 2.11896201 and -2.11896201.

Subproblem 1

x + 1.7 = 2.11896201 Simplifying x + 1.7 = 2.11896201 Reorder the terms: 1.7 + x = 2.11896201 Solving 1.7 + x = 2.11896201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + x = 2.11896201 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = 2.11896201 + -1.7 x = 2.11896201 + -1.7 Combine like terms: 2.11896201 + -1.7 = 0.41896201 x = 0.41896201 Simplifying x = 0.41896201

Subproblem 2

x + 1.7 = -2.11896201 Simplifying x + 1.7 = -2.11896201 Reorder the terms: 1.7 + x = -2.11896201 Solving 1.7 + x = -2.11896201 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.7' to each side of the equation. 1.7 + -1.7 + x = -2.11896201 + -1.7 Combine like terms: 1.7 + -1.7 = 0.0 0.0 + x = -2.11896201 + -1.7 x = -2.11896201 + -1.7 Combine like terms: -2.11896201 + -1.7 = -3.81896201 x = -3.81896201 Simplifying x = -3.81896201

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.41896201, -3.81896201}

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