x(5x-2)=9

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Solution for x(5x-2)=9 equation:


Simplifying
x(5x + -2) = 9

Reorder the terms:
x(-2 + 5x) = 9
(-2 * x + 5x * x) = 9
(-2x + 5x2) = 9

Solving
-2x + 5x2 = 9

Solving for variable 'x'.

Reorder the terms:
-9 + -2x + 5x2 = 9 + -9

Combine like terms: 9 + -9 = 0
-9 + -2x + 5x2 = 0

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

Divide each side by '5'.
-1.8 + -0.4x + x2 = 0

Move the constant term to the right:

Add '1.8' to each side of the equation.
-1.8 + -0.4x + 1.8 + x2 = 0 + 1.8

Reorder the terms:
-1.8 + 1.8 + -0.4x + x2 = 0 + 1.8

Combine like terms: -1.8 + 1.8 = 0.0
0.0 + -0.4x + x2 = 0 + 1.8
-0.4x + x2 = 0 + 1.8

Combine like terms: 0 + 1.8 = 1.8
-0.4x + x2 = 1.8

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 = 1.8 + 0.04

Reorder the terms:
0.04 + -0.4x + x2 = 1.8 + 0.04

Combine like terms: 1.8 + 0.04 = 1.84
0.04 + -0.4x + x2 = 1.84

Factor a perfect square on the left side:
(x + -0.2)(x + -0.2) = 1.84

Calculate the square root of the right side: 1.356465997

Break this problem into two subproblems by setting 
(x + -0.2) equal to 1.356465997 and -1.356465997.

Subproblem 1

x + -0.2 = 1.356465997 Simplifying x + -0.2 = 1.356465997 Reorder the terms: -0.2 + x = 1.356465997 Solving -0.2 + x = 1.356465997 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 = 1.356465997 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 1.356465997 + 0.2 x = 1.356465997 + 0.2 Combine like terms: 1.356465997 + 0.2 = 1.556465997 x = 1.556465997 Simplifying x = 1.556465997

Subproblem 2

x + -0.2 = -1.356465997 Simplifying x + -0.2 = -1.356465997 Reorder the terms: -0.2 + x = -1.356465997 Solving -0.2 + x = -1.356465997 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 = -1.356465997 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -1.356465997 + 0.2 x = -1.356465997 + 0.2 Combine like terms: -1.356465997 + 0.2 = -1.156465997 x = -1.156465997 Simplifying x = -1.156465997

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.556465997, -1.156465997}

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