10x(2x+5)=19

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Solution for 10x(2x+5)=19 equation:


Simplifying
10x(2x + 5) = 19

Reorder the terms:
10x(5 + 2x) = 19
(5 * 10x + 2x * 10x) = 19
(50x + 20x2) = 19

Solving
50x + 20x2 = 19

Solving for variable 'x'.

Reorder the terms:
-19 + 50x + 20x2 = 19 + -19

Combine like terms: 19 + -19 = 0
-19 + 50x + 20x2 = 0

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

Divide each side by '20'.
-0.95 + 2.5x + x2 = 0.0

Move the constant term to the right:

Add '0.95' to each side of the equation.
-0.95 + 2.5x + 0.95 + x2 = 0.0 + 0.95

Reorder the terms:
-0.95 + 0.95 + 2.5x + x2 = 0.0 + 0.95

Combine like terms: -0.95 + 0.95 = 0.00
0.00 + 2.5x + x2 = 0.0 + 0.95
2.5x + x2 = 0.0 + 0.95

Combine like terms: 0.0 + 0.95 = 0.95
2.5x + x2 = 0.95

The x term is 2.5x.  Take half its coefficient (1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
2.5x + 1.5625 + x2 = 0.95 + 1.5625

Reorder the terms:
1.5625 + 2.5x + x2 = 0.95 + 1.5625

Combine like terms: 0.95 + 1.5625 = 2.5125
1.5625 + 2.5x + x2 = 2.5125

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 2.5125

Calculate the square root of the right side: 1.585086748

Break this problem into two subproblems by setting 
(x + 1.25) equal to 1.585086748 and -1.585086748.

Subproblem 1

x + 1.25 = 1.585086748 Simplifying x + 1.25 = 1.585086748 Reorder the terms: 1.25 + x = 1.585086748 Solving 1.25 + x = 1.585086748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = 1.585086748 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = 1.585086748 + -1.25 x = 1.585086748 + -1.25 Combine like terms: 1.585086748 + -1.25 = 0.335086748 x = 0.335086748 Simplifying x = 0.335086748

Subproblem 2

x + 1.25 = -1.585086748 Simplifying x + 1.25 = -1.585086748 Reorder the terms: 1.25 + x = -1.585086748 Solving 1.25 + x = -1.585086748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + x = -1.585086748 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + x = -1.585086748 + -1.25 x = -1.585086748 + -1.25 Combine like terms: -1.585086748 + -1.25 = -2.835086748 x = -2.835086748 Simplifying x = -2.835086748

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.335086748, -2.835086748}

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