2x^2+x=187

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Solution for 2x^2+x=187 equation:


Simplifying
2x2 + x = 187

Reorder the terms:
x + 2x2 = 187

Solving
x + 2x2 = 187

Solving for variable 'x'.

Reorder the terms:
-187 + x + 2x2 = 187 + -187

Combine like terms: 187 + -187 = 0
-187 + x + 2x2 = 0

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

Divide each side by '2'.
-93.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '93.5' to each side of the equation.
-93.5 + 0.5x + 93.5 + x2 = 0 + 93.5

Reorder the terms:
-93.5 + 93.5 + 0.5x + x2 = 0 + 93.5

Combine like terms: -93.5 + 93.5 = 0.0
0.0 + 0.5x + x2 = 0 + 93.5
0.5x + x2 = 0 + 93.5

Combine like terms: 0 + 93.5 = 93.5
0.5x + x2 = 93.5

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

Add '0.25' to each side of the equation.
0.5x + 0.25 + x2 = 93.5 + 0.25

Reorder the terms:
0.25 + 0.5x + x2 = 93.5 + 0.25

Combine like terms: 93.5 + 0.25 = 93.75
0.25 + 0.5x + x2 = 93.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 93.75

Calculate the square root of the right side: 9.682458366

Break this problem into two subproblems by setting 
(x + 0.5) equal to 9.682458366 and -9.682458366.

Subproblem 1

x + 0.5 = 9.682458366 Simplifying x + 0.5 = 9.682458366 Reorder the terms: 0.5 + x = 9.682458366 Solving 0.5 + x = 9.682458366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 9.682458366 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 9.682458366 + -0.5 x = 9.682458366 + -0.5 Combine like terms: 9.682458366 + -0.5 = 9.182458366 x = 9.182458366 Simplifying x = 9.182458366

Subproblem 2

x + 0.5 = -9.682458366 Simplifying x + 0.5 = -9.682458366 Reorder the terms: 0.5 + x = -9.682458366 Solving 0.5 + x = -9.682458366 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -9.682458366 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -9.682458366 + -0.5 x = -9.682458366 + -0.5 Combine like terms: -9.682458366 + -0.5 = -10.182458366 x = -10.182458366 Simplifying x = -10.182458366

Solution

The solution to the problem is based on the solutions from the subproblems. x = {9.182458366, -10.182458366}

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