-.0003x^2-1.4x+34=0

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Solution for -.0003x^2-1.4x+34=0 equation:


Simplifying
-0.0003x2 + -1.4x + 34 = 0

Reorder the terms:
34 + -1.4x + -0.0003x2 = 0

Solving
34 + -1.4x + -0.0003x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.0003 the coefficient of the squared term: 

Divide each side by '-0.0003'.
-113333.3333 + 4666.666667x + x2 = 0

Move the constant term to the right:

Add '113333.3333' to each side of the equation.
-113333.3333 + 4666.666667x + 113333.3333 + x2 = 0 + 113333.3333

Reorder the terms:
-113333.3333 + 113333.3333 + 4666.666667x + x2 = 0 + 113333.3333

Combine like terms: -113333.3333 + 113333.3333 = 0.0000
0.0000 + 4666.666667x + x2 = 0 + 113333.3333
4666.666667x + x2 = 0 + 113333.3333

Combine like terms: 0 + 113333.3333 = 113333.3333
4666.666667x + x2 = 113333.3333

The x term is 4666.666667x.  Take half its coefficient (2333.333334).
Square it (5444444.448) and add it to both sides.

Add '5444444.448' to each side of the equation.
4666.666667x + 5444444.448 + x2 = 113333.3333 + 5444444.448

Reorder the terms:
5444444.448 + 4666.666667x + x2 = 113333.3333 + 5444444.448

Combine like terms: 113333.3333 + 5444444.448 = 5557777.7813
5444444.448 + 4666.666667x + x2 = 5557777.7813

Factor a perfect square on the left side:
(x + 2333.333334)(x + 2333.333334) = 5557777.7813

Calculate the square root of the right side: 2357.493962092

Break this problem into two subproblems by setting 
(x + 2333.333334) equal to 2357.493962092 and -2357.493962092.

Subproblem 1

x + 2333.333334 = 2357.493962092 Simplifying x + 2333.333334 = 2357.493962092 Reorder the terms: 2333.333334 + x = 2357.493962092 Solving 2333.333334 + x = 2357.493962092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2333.333334' to each side of the equation. 2333.333334 + -2333.333334 + x = 2357.493962092 + -2333.333334 Combine like terms: 2333.333334 + -2333.333334 = 0.000000 0.000000 + x = 2357.493962092 + -2333.333334 x = 2357.493962092 + -2333.333334 Combine like terms: 2357.493962092 + -2333.333334 = 24.160628092 x = 24.160628092 Simplifying x = 24.160628092

Subproblem 2

x + 2333.333334 = -2357.493962092 Simplifying x + 2333.333334 = -2357.493962092 Reorder the terms: 2333.333334 + x = -2357.493962092 Solving 2333.333334 + x = -2357.493962092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2333.333334' to each side of the equation. 2333.333334 + -2333.333334 + x = -2357.493962092 + -2333.333334 Combine like terms: 2333.333334 + -2333.333334 = 0.000000 0.000000 + x = -2357.493962092 + -2333.333334 x = -2357.493962092 + -2333.333334 Combine like terms: -2357.493962092 + -2333.333334 = -4690.827296092 x = -4690.827296092 Simplifying x = -4690.827296092

Solution

The solution to the problem is based on the solutions from the subproblems. x = {24.160628092, -4690.827296092}

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