4x+x^2=-2.5

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Solution for 4x+x^2=-2.5 equation:


Simplifying
4x + x2 = -2.5

Solving
4x + x2 = -2.5

Solving for variable 'x'.

Reorder the terms:
2.5 + 4x + x2 = -2.5 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
2.5 + 4x + x2 = 0.0

Begin completing the square.

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 4x + -2.5 + x2 = 0.0 + -2.5

Reorder the terms:
2.5 + -2.5 + 4x + x2 = 0.0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 4x + x2 = 0.0 + -2.5
4x + x2 = 0.0 + -2.5

Combine like terms: 0.0 + -2.5 = -2.5
4x + x2 = -2.5

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -2.5 + 4

Reorder the terms:
4 + 4x + x2 = -2.5 + 4

Combine like terms: -2.5 + 4 = 1.5
4 + 4x + x2 = 1.5

Factor a perfect square on the left side:
(x + 2)(x + 2) = 1.5

Calculate the square root of the right side: 1.224744871

Break this problem into two subproblems by setting 
(x + 2) equal to 1.224744871 and -1.224744871.

Subproblem 1

x + 2 = 1.224744871 Simplifying x + 2 = 1.224744871 Reorder the terms: 2 + x = 1.224744871 Solving 2 + x = 1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.224744871 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.224744871 + -2 x = 1.224744871 + -2 Combine like terms: 1.224744871 + -2 = -0.775255129 x = -0.775255129 Simplifying x = -0.775255129

Subproblem 2

x + 2 = -1.224744871 Simplifying x + 2 = -1.224744871 Reorder the terms: 2 + x = -1.224744871 Solving 2 + x = -1.224744871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.224744871 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.224744871 + -2 x = -1.224744871 + -2 Combine like terms: -1.224744871 + -2 = -3.224744871 x = -3.224744871 Simplifying x = -3.224744871

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.775255129, -3.224744871}

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