40x(x-.06)=2.00

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Solution for 40x(x-.06)=2.00 equation:


Simplifying
40x(x + -0.06) = 2.00

Reorder the terms:
40x(-0.06 + x) = 2.00
(-0.06 * 40x + x * 40x) = 2.00
(-2.4x + 40x2) = 2.00

Solving
-2.4x + 40x2 = 2.00

Solving for variable 'x'.

Reorder the terms:
-2.00 + -2.4x + 40x2 = 2.00 + -2.00

Combine like terms: 2.00 + -2.00 = 0.00
-2.00 + -2.4x + 40x2 = 0.00

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

Divide each side by '40'.
-0.05 + -0.06x + x2 = 0.00

Move the constant term to the right:

Add '0.05' to each side of the equation.
-0.05 + -0.06x + 0.05 + x2 = 0.00 + 0.05

Reorder the terms:
-0.05 + 0.05 + -0.06x + x2 = 0.00 + 0.05

Combine like terms: -0.05 + 0.05 = 0.00
0.00 + -0.06x + x2 = 0.00 + 0.05
-0.06x + x2 = 0.00 + 0.05

Combine like terms: 0.00 + 0.05 = 0.05
-0.06x + x2 = 0.05

The x term is -0.06x.  Take half its coefficient (-0.03).
Square it (0.0009) and add it to both sides.

Add '0.0009' to each side of the equation.
-0.06x + 0.0009 + x2 = 0.05 + 0.0009

Reorder the terms:
0.0009 + -0.06x + x2 = 0.05 + 0.0009

Combine like terms: 0.05 + 0.0009 = 0.0509
0.0009 + -0.06x + x2 = 0.0509

Factor a perfect square on the left side:
(x + -0.03)(x + -0.03) = 0.0509

Calculate the square root of the right side: 0.225610283

Break this problem into two subproblems by setting 
(x + -0.03) equal to 0.225610283 and -0.225610283.

Subproblem 1

x + -0.03 = 0.225610283 Simplifying x + -0.03 = 0.225610283 Reorder the terms: -0.03 + x = 0.225610283 Solving -0.03 + x = 0.225610283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03' to each side of the equation. -0.03 + 0.03 + x = 0.225610283 + 0.03 Combine like terms: -0.03 + 0.03 = 0.00 0.00 + x = 0.225610283 + 0.03 x = 0.225610283 + 0.03 Combine like terms: 0.225610283 + 0.03 = 0.255610283 x = 0.255610283 Simplifying x = 0.255610283

Subproblem 2

x + -0.03 = -0.225610283 Simplifying x + -0.03 = -0.225610283 Reorder the terms: -0.03 + x = -0.225610283 Solving -0.03 + x = -0.225610283 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03' to each side of the equation. -0.03 + 0.03 + x = -0.225610283 + 0.03 Combine like terms: -0.03 + 0.03 = 0.00 0.00 + x = -0.225610283 + 0.03 x = -0.225610283 + 0.03 Combine like terms: -0.225610283 + 0.03 = -0.195610283 x = -0.195610283 Simplifying x = -0.195610283

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.255610283, -0.195610283}

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