x^2+0.02x=0.07

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Solution for x^2+0.02x=0.07 equation: 


Simplifying
x2 + 0.02x = 0.07

Reorder the terms:
0.02x + x2 = 0.07

Solving
0.02x + x2 = 0.07

Solving for variable 'x'.

Reorder the terms:
-0.07 + 0.02x + x2 = 0.07 + -0.07

Combine like terms: 0.07 + -0.07 = 0.00
-0.07 + 0.02x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.07' to each side of the equation.
-0.07 + 0.02x + 0.07 + x2 = 0.00 + 0.07

Reorder the terms:
-0.07 + 0.07 + 0.02x + x2 = 0.00 + 0.07

Combine like terms: -0.07 + 0.07 = 0.00
0.00 + 0.02x + x2 = 0.00 + 0.07
0.02x + x2 = 0.00 + 0.07

Combine like terms: 0.00 + 0.07 = 0.07
0.02x + x2 = 0.07

The x term is 0.02x.  Take half its coefficient (0.01).
Square it (0.0001) and add it to both sides.

Add '0.0001' to each side of the equation.
0.02x + 0.0001 + x2 = 0.07 + 0.0001

Reorder the terms:
0.0001 + 0.02x + x2 = 0.07 + 0.0001

Combine like terms: 0.07 + 0.0001 = 0.0701
0.0001 + 0.02x + x2 = 0.0701

Factor a perfect square on the left side:
(x + 0.01)(x + 0.01) = 0.0701

Calculate the square root of the right side: 0.264764046

Break this problem into two subproblems by setting 
(x + 0.01) equal to 0.264764046 and -0.264764046.


Subproblem 1
x + 0.01 = 0.264764046

Simplifying
x + 0.01 = 0.264764046

Reorder the terms:
0.01 + x = 0.264764046

Solving
0.01 + x = 0.264764046

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.01' to each side of the equation.
0.01 + -0.01 + x = 0.264764046 + -0.01

Combine like terms: 0.01 + -0.01 = 0.00
0.00 + x = 0.264764046 + -0.01
x = 0.264764046 + -0.01

Combine like terms: 0.264764046 + -0.01 = 0.254764046
x = 0.254764046

Simplifying
x = 0.254764046


Subproblem 2
x + 0.01 = -0.264764046

Simplifying
x + 0.01 = -0.264764046

Reorder the terms:
0.01 + x = -0.264764046

Solving
0.01 + x = -0.264764046

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-0.01' to each side of the equation.
0.01 + -0.01 + x = -0.264764046 + -0.01

Combine like terms: 0.01 + -0.01 = 0.00
0.00 + x = -0.264764046 + -0.01
x = -0.264764046 + -0.01

Combine like terms: -0.264764046 + -0.01 = -0.274764046
x = -0.274764046

Simplifying
x = -0.274764046


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.254764046, -0.274764046}

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