2x^2-10x+2=2x-7

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Solution for 2x^2-10x+2=2x-7 equation:


Simplifying
2x2 + -10x + 2 = 2x + -7

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

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

Solving
2 + -10x + 2x2 = -7 + 2x

Solving for variable 'x'.

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

Combine like terms: 2 + 7 = 9
9 + -10x + -2x + 2x2 = -7 + 2x + 7 + -2x

Combine like terms: -10x + -2x = -12x
9 + -12x + 2x2 = -7 + 2x + 7 + -2x

Reorder the terms:
9 + -12x + 2x2 = -7 + 7 + 2x + -2x

Combine like terms: -7 + 7 = 0
9 + -12x + 2x2 = 0 + 2x + -2x
9 + -12x + 2x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
9 + -12x + 2x2 = 0

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

Divide each side by '2'.
4.5 + -6x + x2 = 0

Move the constant term to the right:

Add '-4.5' to each side of the equation.
4.5 + -6x + -4.5 + x2 = 0 + -4.5

Reorder the terms:
4.5 + -4.5 + -6x + x2 = 0 + -4.5

Combine like terms: 4.5 + -4.5 = 0.0
0.0 + -6x + x2 = 0 + -4.5
-6x + x2 = 0 + -4.5

Combine like terms: 0 + -4.5 = -4.5
-6x + x2 = -4.5

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 = -4.5 + 9

Reorder the terms:
9 + -6x + x2 = -4.5 + 9

Combine like terms: -4.5 + 9 = 4.5
9 + -6x + x2 = 4.5

Factor a perfect square on the left side:
(x + -3)(x + -3) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(x + -3) equal to 2.121320344 and -2.121320344.

Subproblem 1

x + -3 = 2.121320344 Simplifying x + -3 = 2.121320344 Reorder the terms: -3 + x = 2.121320344 Solving -3 + x = 2.121320344 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 = 2.121320344 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.121320344 + 3 x = 2.121320344 + 3 Combine like terms: 2.121320344 + 3 = 5.121320344 x = 5.121320344 Simplifying x = 5.121320344

Subproblem 2

x + -3 = -2.121320344 Simplifying x + -3 = -2.121320344 Reorder the terms: -3 + x = -2.121320344 Solving -3 + x = -2.121320344 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 = -2.121320344 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.121320344 + 3 x = -2.121320344 + 3 Combine like terms: -2.121320344 + 3 = 0.878679656 x = 0.878679656 Simplifying x = 0.878679656

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.121320344, 0.878679656}

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