x^2+.07x-.007=0

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Solution for x^2+.07x-.007=0 equation:


Simplifying
x2 + 0.07x + -0.007 = 0

Reorder the terms:
-0.007 + 0.07x + x2 = 0

Solving
-0.007 + 0.07x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.007' to each side of the equation.
-0.007 + 0.07x + 0.007 + x2 = 0 + 0.007

Reorder the terms:
-0.007 + 0.007 + 0.07x + x2 = 0 + 0.007

Combine like terms: -0.007 + 0.007 = 0.000
0.000 + 0.07x + x2 = 0 + 0.007
0.07x + x2 = 0 + 0.007

Combine like terms: 0 + 0.007 = 0.007
0.07x + x2 = 0.007

The x term is 0.07x.  Take half its coefficient (0.035).
Square it (0.001225) and add it to both sides.

Add '0.001225' to each side of the equation.
0.07x + 0.001225 + x2 = 0.007 + 0.001225

Reorder the terms:
0.001225 + 0.07x + x2 = 0.007 + 0.001225

Combine like terms: 0.007 + 0.001225 = 0.008225
0.001225 + 0.07x + x2 = 0.008225

Factor a perfect square on the left side:
(x + 0.035)(x + 0.035) = 0.008225

Calculate the square root of the right side: 0.090691786

Break this problem into two subproblems by setting 
(x + 0.035) equal to 0.090691786 and -0.090691786.

Subproblem 1

x + 0.035 = 0.090691786 Simplifying x + 0.035 = 0.090691786 Reorder the terms: 0.035 + x = 0.090691786 Solving 0.035 + x = 0.090691786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.035' to each side of the equation. 0.035 + -0.035 + x = 0.090691786 + -0.035 Combine like terms: 0.035 + -0.035 = 0.000 0.000 + x = 0.090691786 + -0.035 x = 0.090691786 + -0.035 Combine like terms: 0.090691786 + -0.035 = 0.055691786 x = 0.055691786 Simplifying x = 0.055691786

Subproblem 2

x + 0.035 = -0.090691786 Simplifying x + 0.035 = -0.090691786 Reorder the terms: 0.035 + x = -0.090691786 Solving 0.035 + x = -0.090691786 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.035' to each side of the equation. 0.035 + -0.035 + x = -0.090691786 + -0.035 Combine like terms: 0.035 + -0.035 = 0.000 0.000 + x = -0.090691786 + -0.035 x = -0.090691786 + -0.035 Combine like terms: -0.090691786 + -0.035 = -0.125691786 x = -0.125691786 Simplifying x = -0.125691786

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.055691786, -0.125691786}

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