2x*x=17+x

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Solution for 2x*x=17+x equation:


Simplifying
2x * x = 17 + x

Multiply x * x
2x2 = 17 + x

Solving
2x2 = 17 + x

Solving for variable 'x'.

Reorder the terms:
-17 + -1x + 2x2 = 17 + x + -17 + -1x

Reorder the terms:
-17 + -1x + 2x2 = 17 + -17 + x + -1x

Combine like terms: 17 + -17 = 0
-17 + -1x + 2x2 = 0 + x + -1x
-17 + -1x + 2x2 = x + -1x

Combine like terms: x + -1x = 0
-17 + -1x + 2x2 = 0

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

Divide each side by '2'.
-8.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '8.5' to each side of the equation.
-8.5 + -0.5x + 8.5 + x2 = 0 + 8.5

Reorder the terms:
-8.5 + 8.5 + -0.5x + x2 = 0 + 8.5

Combine like terms: -8.5 + 8.5 = 0.0
0.0 + -0.5x + x2 = 0 + 8.5
-0.5x + x2 = 0 + 8.5

Combine like terms: 0 + 8.5 = 8.5
-0.5x + x2 = 8.5

The x term is -0.5x.  Take half its coefficient (-0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
-0.5x + 0.0625 + x2 = 8.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 8.5 + 0.0625

Combine like terms: 8.5 + 0.0625 = 8.5625
0.0625 + -0.5x + x2 = 8.5625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 8.5625

Calculate the square root of the right side: 2.926174978

Break this problem into two subproblems by setting 
(x + -0.25) equal to 2.926174978 and -2.926174978.

Subproblem 1

x + -0.25 = 2.926174978 Simplifying x + -0.25 = 2.926174978 Reorder the terms: -0.25 + x = 2.926174978 Solving -0.25 + x = 2.926174978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.926174978 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.926174978 + 0.25 x = 2.926174978 + 0.25 Combine like terms: 2.926174978 + 0.25 = 3.176174978 x = 3.176174978 Simplifying x = 3.176174978

Subproblem 2

x + -0.25 = -2.926174978 Simplifying x + -0.25 = -2.926174978 Reorder the terms: -0.25 + x = -2.926174978 Solving -0.25 + x = -2.926174978 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.926174978 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.926174978 + 0.25 x = -2.926174978 + 0.25 Combine like terms: -2.926174978 + 0.25 = -2.676174978 x = -2.676174978 Simplifying x = -2.676174978

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.176174978, -2.676174978}

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