23.5=x^2+4x

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Solution for 23.5=x^2+4x equation:


Simplifying
23.5 = x2 + 4x

Reorder the terms:
23.5 = 4x + x2

Solving
23.5 = 4x + x2

Solving for variable 'x'.

Reorder the terms:
23.5 + -4x + -1x2 = 4x + -4x + x2 + -1x2

Combine like terms: 4x + -4x = 0
23.5 + -4x + -1x2 = 0 + x2 + -1x2
23.5 + -4x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
23.5 + -4x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-23.5 + 4x + x2 = 0

Move the constant term to the right:

Add '23.5' to each side of the equation.
-23.5 + 4x + 23.5 + x2 = 0 + 23.5

Reorder the terms:
-23.5 + 23.5 + 4x + x2 = 0 + 23.5

Combine like terms: -23.5 + 23.5 = 0.0
0.0 + 4x + x2 = 0 + 23.5
4x + x2 = 0 + 23.5

Combine like terms: 0 + 23.5 = 23.5
4x + x2 = 23.5

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 = 23.5 + 4

Reorder the terms:
4 + 4x + x2 = 23.5 + 4

Combine like terms: 23.5 + 4 = 27.5
4 + 4x + x2 = 27.5

Factor a perfect square on the left side:
(x + 2)(x + 2) = 27.5

Calculate the square root of the right side: 5.244044241

Break this problem into two subproblems by setting 
(x + 2) equal to 5.244044241 and -5.244044241.

Subproblem 1

x + 2 = 5.244044241 Simplifying x + 2 = 5.244044241 Reorder the terms: 2 + x = 5.244044241 Solving 2 + x = 5.244044241 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 = 5.244044241 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.244044241 + -2 x = 5.244044241 + -2 Combine like terms: 5.244044241 + -2 = 3.244044241 x = 3.244044241 Simplifying x = 3.244044241

Subproblem 2

x + 2 = -5.244044241 Simplifying x + 2 = -5.244044241 Reorder the terms: 2 + x = -5.244044241 Solving 2 + x = -5.244044241 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 = -5.244044241 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.244044241 + -2 x = -5.244044241 + -2 Combine like terms: -5.244044241 + -2 = -7.244044241 x = -7.244044241 Simplifying x = -7.244044241

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.244044241, -7.244044241}

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