(0.5x+2)*x-5=30

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Solution for (0.5x+2)*x-5=30 equation:


Simplifying
(0.5x + 2) * x + -5 = 30

Reorder the terms:
(2 + 0.5x) * x + -5 = 30

Reorder the terms for easier multiplication:
x(2 + 0.5x) + -5 = 30
(2 * x + 0.5x * x) + -5 = 30
(2x + 0.5x2) + -5 = 30

Reorder the terms:
-5 + 2x + 0.5x2 = 30

Solving
-5 + 2x + 0.5x2 = 30

Solving for variable 'x'.

Reorder the terms:
-5 + -30 + 2x + 0.5x2 = 30 + -30

Combine like terms: -5 + -30 = -35
-35 + 2x + 0.5x2 = 30 + -30

Combine like terms: 30 + -30 = 0
-35 + 2x + 0.5x2 = 0

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

Divide each side by '0.5'.
-70 + 4x + x2 = 0

Move the constant term to the right:

Add '70' to each side of the equation.
-70 + 4x + 70 + x2 = 0 + 70

Reorder the terms:
-70 + 70 + 4x + x2 = 0 + 70

Combine like terms: -70 + 70 = 0
0 + 4x + x2 = 0 + 70
4x + x2 = 0 + 70

Combine like terms: 0 + 70 = 70
4x + x2 = 70

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 = 70 + 4

Reorder the terms:
4 + 4x + x2 = 70 + 4

Combine like terms: 70 + 4 = 74
4 + 4x + x2 = 74

Factor a perfect square on the left side:
(x + 2)(x + 2) = 74

Calculate the square root of the right side: 8.602325267

Break this problem into two subproblems by setting 
(x + 2) equal to 8.602325267 and -8.602325267.

Subproblem 1

x + 2 = 8.602325267 Simplifying x + 2 = 8.602325267 Reorder the terms: 2 + x = 8.602325267 Solving 2 + x = 8.602325267 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 = 8.602325267 + -2 Combine like terms: 2 + -2 = 0 0 + x = 8.602325267 + -2 x = 8.602325267 + -2 Combine like terms: 8.602325267 + -2 = 6.602325267 x = 6.602325267 Simplifying x = 6.602325267

Subproblem 2

x + 2 = -8.602325267 Simplifying x + 2 = -8.602325267 Reorder the terms: 2 + x = -8.602325267 Solving 2 + x = -8.602325267 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 = -8.602325267 + -2 Combine like terms: 2 + -2 = 0 0 + x = -8.602325267 + -2 x = -8.602325267 + -2 Combine like terms: -8.602325267 + -2 = -10.602325267 x = -10.602325267 Simplifying x = -10.602325267

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.602325267, -10.602325267}

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