2x+x^2=4.875

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Solution for 2x+x^2=4.875 equation:


Simplifying
2x + x2 = 4.875

Solving
2x + x2 = 4.875

Solving for variable 'x'.

Reorder the terms:
-4.875 + 2x + x2 = 4.875 + -4.875

Combine like terms: 4.875 + -4.875 = 0.000
-4.875 + 2x + x2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '4.875' to each side of the equation.
-4.875 + 2x + 4.875 + x2 = 0.000 + 4.875

Reorder the terms:
-4.875 + 4.875 + 2x + x2 = 0.000 + 4.875

Combine like terms: -4.875 + 4.875 = 0.000
0.000 + 2x + x2 = 0.000 + 4.875
2x + x2 = 0.000 + 4.875

Combine like terms: 0.000 + 4.875 = 4.875
2x + x2 = 4.875

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 4.875 + 1

Reorder the terms:
1 + 2x + x2 = 4.875 + 1

Combine like terms: 4.875 + 1 = 5.875
1 + 2x + x2 = 5.875

Factor a perfect square on the left side:
(x + 1)(x + 1) = 5.875

Calculate the square root of the right side: 2.423839929

Break this problem into two subproblems by setting 
(x + 1) equal to 2.423839929 and -2.423839929.

Subproblem 1

x + 1 = 2.423839929 Simplifying x + 1 = 2.423839929 Reorder the terms: 1 + x = 2.423839929 Solving 1 + x = 2.423839929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.423839929 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.423839929 + -1 x = 2.423839929 + -1 Combine like terms: 2.423839929 + -1 = 1.423839929 x = 1.423839929 Simplifying x = 1.423839929

Subproblem 2

x + 1 = -2.423839929 Simplifying x + 1 = -2.423839929 Reorder the terms: 1 + x = -2.423839929 Solving 1 + x = -2.423839929 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.423839929 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.423839929 + -1 x = -2.423839929 + -1 Combine like terms: -2.423839929 + -1 = -3.423839929 x = -3.423839929 Simplifying x = -3.423839929

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.423839929, -3.423839929}

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