2x^2+2x+1=50

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Solution for 2x^2+2x+1=50 equation:


Simplifying
2x2 + 2x + 1 = 50

Reorder the terms:
1 + 2x + 2x2 = 50

Solving
1 + 2x + 2x2 = 50

Solving for variable 'x'.

Reorder the terms:
1 + -50 + 2x + 2x2 = 50 + -50

Combine like terms: 1 + -50 = -49
-49 + 2x + 2x2 = 50 + -50

Combine like terms: 50 + -50 = 0
-49 + 2x + 2x2 = 0

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

Divide each side by '2'.
-24.5 + x + x2 = 0

Move the constant term to the right:

Add '24.5' to each side of the equation.
-24.5 + x + 24.5 + x2 = 0 + 24.5

Reorder the terms:
-24.5 + 24.5 + x + x2 = 0 + 24.5

Combine like terms: -24.5 + 24.5 = 0.0
0.0 + x + x2 = 0 + 24.5
x + x2 = 0 + 24.5

Combine like terms: 0 + 24.5 = 24.5
x + x2 = 24.5

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.
 + 0.25 + x2 = 24.5 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 24.5 + 0.25

Combine like terms: 24.5 + 0.25 = 24.75
1.25 + x2 = 24.75

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 24.75

Calculate the square root of the right side: 4.974937186

Break this problem into two subproblems by setting 
(x + 0.5) equal to 4.974937186 and -4.974937186.

Subproblem 1

x + 0.5 = 4.974937186 Simplifying x + 0.5 = 4.974937186 Reorder the terms: 0.5 + x = 4.974937186 Solving 0.5 + x = 4.974937186 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 = 4.974937186 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 4.974937186 + -0.5 x = 4.974937186 + -0.5 Combine like terms: 4.974937186 + -0.5 = 4.474937186 x = 4.474937186 Simplifying x = 4.474937186

Subproblem 2

x + 0.5 = -4.974937186 Simplifying x + 0.5 = -4.974937186 Reorder the terms: 0.5 + x = -4.974937186 Solving 0.5 + x = -4.974937186 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 = -4.974937186 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -4.974937186 + -0.5 x = -4.974937186 + -0.5 Combine like terms: -4.974937186 + -0.5 = -5.474937186 x = -5.474937186 Simplifying x = -5.474937186

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.474937186, -5.474937186}

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