2x(5x-2)=21

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Solution for 2x(5x-2)=21 equation:


Simplifying
2x(5x + -2) = 21

Reorder the terms:
2x(-2 + 5x) = 21
(-2 * 2x + 5x * 2x) = 21
(-4x + 10x2) = 21

Solving
-4x + 10x2 = 21

Solving for variable 'x'.

Reorder the terms:
-21 + -4x + 10x2 = 21 + -21

Combine like terms: 21 + -21 = 0
-21 + -4x + 10x2 = 0

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

Divide each side by '10'.
-2.1 + -0.4x + x2 = 0.0

Move the constant term to the right:

Add '2.1' to each side of the equation.
-2.1 + -0.4x + 2.1 + x2 = 0.0 + 2.1

Reorder the terms:
-2.1 + 2.1 + -0.4x + x2 = 0.0 + 2.1

Combine like terms: -2.1 + 2.1 = 0.0
0.0 + -0.4x + x2 = 0.0 + 2.1
-0.4x + x2 = 0.0 + 2.1

Combine like terms: 0.0 + 2.1 = 2.1
-0.4x + x2 = 2.1

The x term is -0.4x.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4x + 0.04 + x2 = 2.1 + 0.04

Reorder the terms:
0.04 + -0.4x + x2 = 2.1 + 0.04

Combine like terms: 2.1 + 0.04 = 2.14
0.04 + -0.4x + x2 = 2.14

Factor a perfect square on the left side:
(x + -0.2)(x + -0.2) = 2.14

Calculate the square root of the right side: 1.462873884

Break this problem into two subproblems by setting 
(x + -0.2) equal to 1.462873884 and -1.462873884.

Subproblem 1

x + -0.2 = 1.462873884 Simplifying x + -0.2 = 1.462873884 Reorder the terms: -0.2 + x = 1.462873884 Solving -0.2 + x = 1.462873884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 1.462873884 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 1.462873884 + 0.2 x = 1.462873884 + 0.2 Combine like terms: 1.462873884 + 0.2 = 1.662873884 x = 1.662873884 Simplifying x = 1.662873884

Subproblem 2

x + -0.2 = -1.462873884 Simplifying x + -0.2 = -1.462873884 Reorder the terms: -0.2 + x = -1.462873884 Solving -0.2 + x = -1.462873884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -1.462873884 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -1.462873884 + 0.2 x = -1.462873884 + 0.2 Combine like terms: -1.462873884 + 0.2 = -1.262873884 x = -1.262873884 Simplifying x = -1.262873884

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.662873884, -1.262873884}

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