2x(4+5x)=5+10

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Solution for 2x(4+5x)=5+10 equation:


Simplifying
2x(4 + 5x) = 5 + 10
(4 * 2x + 5x * 2x) = 5 + 10
(8x + 10x2) = 5 + 10

Combine like terms: 5 + 10 = 15
8x + 10x2 = 15

Solving
8x + 10x2 = 15

Solving for variable 'x'.

Reorder the terms:
-15 + 8x + 10x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-15 + 8x + 10x2 = 0

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

Divide each side by '10'.
-1.5 + 0.8x + x2 = 0.0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 0.8x + 1.5 + x2 = 0.0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 0.8x + x2 = 0.0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 0.8x + x2 = 0.0 + 1.5
0.8x + x2 = 0.0 + 1.5

Combine like terms: 0.0 + 1.5 = 1.5
0.8x + x2 = 1.5

The x term is 0.8x.  Take half its coefficient (0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
0.8x + 0.16 + x2 = 1.5 + 0.16

Reorder the terms:
0.16 + 0.8x + x2 = 1.5 + 0.16

Combine like terms: 1.5 + 0.16 = 1.66
0.16 + 0.8x + x2 = 1.66

Factor a perfect square on the left side:
(x + 0.4)(x + 0.4) = 1.66

Calculate the square root of the right side: 1.288409873

Break this problem into two subproblems by setting 
(x + 0.4) equal to 1.288409873 and -1.288409873.

Subproblem 1

x + 0.4 = 1.288409873 Simplifying x + 0.4 = 1.288409873 Reorder the terms: 0.4 + x = 1.288409873 Solving 0.4 + x = 1.288409873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = 1.288409873 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = 1.288409873 + -0.4 x = 1.288409873 + -0.4 Combine like terms: 1.288409873 + -0.4 = 0.888409873 x = 0.888409873 Simplifying x = 0.888409873

Subproblem 2

x + 0.4 = -1.288409873 Simplifying x + 0.4 = -1.288409873 Reorder the terms: 0.4 + x = -1.288409873 Solving 0.4 + x = -1.288409873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4' to each side of the equation. 0.4 + -0.4 + x = -1.288409873 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + x = -1.288409873 + -0.4 x = -1.288409873 + -0.4 Combine like terms: -1.288409873 + -0.4 = -1.688409873 x = -1.688409873 Simplifying x = -1.688409873

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.888409873, -1.688409873}

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