2x^2-x-35=0

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Solution for 2x^2-x-35=0 equation:


Simplifying
2x2 + -1x + -35 = 0

Reorder the terms:
-35 + -1x + 2x2 = 0

Solving
-35 + -1x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
-17.5 + -0.5x + x2 = 0

Move the constant term to the right:

Add '17.5' to each side of the equation.
-17.5 + -0.5x + 17.5 + x2 = 0 + 17.5

Reorder the terms:
-17.5 + 17.5 + -0.5x + x2 = 0 + 17.5

Combine like terms: -17.5 + 17.5 = 0.0
0.0 + -0.5x + x2 = 0 + 17.5
-0.5x + x2 = 0 + 17.5

Combine like terms: 0 + 17.5 = 17.5
-0.5x + x2 = 17.5

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 = 17.5 + 0.0625

Reorder the terms:
0.0625 + -0.5x + x2 = 17.5 + 0.0625

Combine like terms: 17.5 + 0.0625 = 17.5625
0.0625 + -0.5x + x2 = 17.5625

Factor a perfect square on the left side:
(x + -0.25)(x + -0.25) = 17.5625

Calculate the square root of the right side: 4.190763654

Break this problem into two subproblems by setting 
(x + -0.25) equal to 4.190763654 and -4.190763654.

Subproblem 1

x + -0.25 = 4.190763654 Simplifying x + -0.25 = 4.190763654 Reorder the terms: -0.25 + x = 4.190763654 Solving -0.25 + x = 4.190763654 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 = 4.190763654 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 4.190763654 + 0.25 x = 4.190763654 + 0.25 Combine like terms: 4.190763654 + 0.25 = 4.440763654 x = 4.440763654 Simplifying x = 4.440763654

Subproblem 2

x + -0.25 = -4.190763654 Simplifying x + -0.25 = -4.190763654 Reorder the terms: -0.25 + x = -4.190763654 Solving -0.25 + x = -4.190763654 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 = -4.190763654 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -4.190763654 + 0.25 x = -4.190763654 + 0.25 Combine like terms: -4.190763654 + 0.25 = -3.940763654 x = -3.940763654 Simplifying x = -3.940763654

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.440763654, -3.940763654}

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