4x^2+0.5x=0.02

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Solution for 4x^2+0.5x=0.02 equation:


Simplifying
4x2 + 0.5x = 0.02

Reorder the terms:
0.5x + 4x2 = 0.02

Solving
0.5x + 4x2 = 0.02

Solving for variable 'x'.

Reorder the terms:
-0.02 + 0.5x + 4x2 = 0.02 + -0.02

Combine like terms: 0.02 + -0.02 = 0.00
-0.02 + 0.5x + 4x2 = 0.00

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

Divide each side by '4'.
-0.005 + 0.125x + x2 = 0.00

Move the constant term to the right:

Add '0.005' to each side of the equation.
-0.005 + 0.125x + 0.005 + x2 = 0.00 + 0.005

Reorder the terms:
-0.005 + 0.005 + 0.125x + x2 = 0.00 + 0.005

Combine like terms: -0.005 + 0.005 = 0.000
0.000 + 0.125x + x2 = 0.00 + 0.005
0.125x + x2 = 0.00 + 0.005

Combine like terms: 0.00 + 0.005 = 0.005
0.125x + x2 = 0.005

The x term is 0.125x.  Take half its coefficient (0.0625).
Square it (0.00390625) and add it to both sides.

Add '0.00390625' to each side of the equation.
0.125x + 0.00390625 + x2 = 0.005 + 0.00390625

Reorder the terms:
0.00390625 + 0.125x + x2 = 0.005 + 0.00390625

Combine like terms: 0.005 + 0.00390625 = 0.00890625
0.00390625 + 0.125x + x2 = 0.00890625

Factor a perfect square on the left side:
(x + 0.0625)(x + 0.0625) = 0.00890625

Calculate the square root of the right side: 0.09437293

Break this problem into two subproblems by setting 
(x + 0.0625) equal to 0.09437293 and -0.09437293.

Subproblem 1

x + 0.0625 = 0.09437293 Simplifying x + 0.0625 = 0.09437293 Reorder the terms: 0.0625 + x = 0.09437293 Solving 0.0625 + x = 0.09437293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = 0.09437293 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = 0.09437293 + -0.0625 x = 0.09437293 + -0.0625 Combine like terms: 0.09437293 + -0.0625 = 0.03187293 x = 0.03187293 Simplifying x = 0.03187293

Subproblem 2

x + 0.0625 = -0.09437293 Simplifying x + 0.0625 = -0.09437293 Reorder the terms: 0.0625 + x = -0.09437293 Solving 0.0625 + x = -0.09437293 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0625' to each side of the equation. 0.0625 + -0.0625 + x = -0.09437293 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + x = -0.09437293 + -0.0625 x = -0.09437293 + -0.0625 Combine like terms: -0.09437293 + -0.0625 = -0.15687293 x = -0.15687293 Simplifying x = -0.15687293

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.03187293, -0.15687293}

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