2(x^2)-7x=1

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Solution for 2(x^2)-7x=1 equation:


Simplifying
2(x2) + -7x = 1

Reorder the terms:
-7x + 2x2 = 1

Solving
-7x + 2x2 = 1

Solving for variable 'x'.

Reorder the terms:
-1 + -7x + 2x2 = 1 + -1

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

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

Divide each side by '2'.
-0.5 + -3.5x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + -3.5x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + -3.5x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + -3.5x + x2 = 0 + 0.5
-3.5x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
-3.5x + x2 = 0.5

The x term is -3.5x.  Take half its coefficient (-1.75).
Square it (3.0625) and add it to both sides.

Add '3.0625' to each side of the equation.
-3.5x + 3.0625 + x2 = 0.5 + 3.0625

Reorder the terms:
3.0625 + -3.5x + x2 = 0.5 + 3.0625

Combine like terms: 0.5 + 3.0625 = 3.5625
3.0625 + -3.5x + x2 = 3.5625

Factor a perfect square on the left side:
(x + -1.75)(x + -1.75) = 3.5625

Calculate the square root of the right side: 1.887458609

Break this problem into two subproblems by setting 
(x + -1.75) equal to 1.887458609 and -1.887458609.

Subproblem 1

x + -1.75 = 1.887458609 Simplifying x + -1.75 = 1.887458609 Reorder the terms: -1.75 + x = 1.887458609 Solving -1.75 + x = 1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 1.887458609 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 1.887458609 + 1.75 x = 1.887458609 + 1.75 Combine like terms: 1.887458609 + 1.75 = 3.637458609 x = 3.637458609 Simplifying x = 3.637458609

Subproblem 2

x + -1.75 = -1.887458609 Simplifying x + -1.75 = -1.887458609 Reorder the terms: -1.75 + x = -1.887458609 Solving -1.75 + x = -1.887458609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -1.887458609 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -1.887458609 + 1.75 x = -1.887458609 + 1.75 Combine like terms: -1.887458609 + 1.75 = -0.137458609 x = -0.137458609 Simplifying x = -0.137458609

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.637458609, -0.137458609}

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