10x-6+2x^2=1

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Solution for 10x-6+2x^2=1 equation:


Simplifying
10x + -6 + 2x2 = 1

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

Solving
-6 + 10x + 2x2 = 1

Solving for variable 'x'.

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

Combine like terms: -6 + -1 = -7
-7 + 10x + 2x2 = 1 + -1

Combine like terms: 1 + -1 = 0
-7 + 10x + 2x2 = 0

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

Divide each side by '2'.
-3.5 + 5x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 5x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 5x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 5x + x2 = 0 + 3.5
5x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
5x + x2 = 3.5

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 3.5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 3.5 + 6.25

Combine like terms: 3.5 + 6.25 = 9.75
6.25 + 5x + x2 = 9.75

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 9.75

Calculate the square root of the right side: 3.122498999

Break this problem into two subproblems by setting 
(x + 2.5) equal to 3.122498999 and -3.122498999.

Subproblem 1

x + 2.5 = 3.122498999 Simplifying x + 2.5 = 3.122498999 Reorder the terms: 2.5 + x = 3.122498999 Solving 2.5 + x = 3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 3.122498999 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 3.122498999 + -2.5 x = 3.122498999 + -2.5 Combine like terms: 3.122498999 + -2.5 = 0.622498999 x = 0.622498999 Simplifying x = 0.622498999

Subproblem 2

x + 2.5 = -3.122498999 Simplifying x + 2.5 = -3.122498999 Reorder the terms: 2.5 + x = -3.122498999 Solving 2.5 + x = -3.122498999 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -3.122498999 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -3.122498999 + -2.5 x = -3.122498999 + -2.5 Combine like terms: -3.122498999 + -2.5 = -5.622498999 x = -5.622498999 Simplifying x = -5.622498999

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.622498999, -5.622498999}

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