.1x^2+60x+1000=0

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Solution for .1x^2+60x+1000=0 equation:


Simplifying
0.1x2 + 60x + 1000 = 0

Reorder the terms:
1000 + 60x + 0.1x2 = 0

Solving
1000 + 60x + 0.1x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.1'.
10000 + 600x + x2 = 0

Move the constant term to the right:

Add '-10000' to each side of the equation.
10000 + 600x + -10000 + x2 = 0 + -10000

Reorder the terms:
10000 + -10000 + 600x + x2 = 0 + -10000

Combine like terms: 10000 + -10000 = 0
0 + 600x + x2 = 0 + -10000
600x + x2 = 0 + -10000

Combine like terms: 0 + -10000 = -10000
600x + x2 = -10000

The x term is 600x.  Take half its coefficient (300).
Square it (90000) and add it to both sides.

Add '90000' to each side of the equation.
600x + 90000 + x2 = -10000 + 90000

Reorder the terms:
90000 + 600x + x2 = -10000 + 90000

Combine like terms: -10000 + 90000 = 80000
90000 + 600x + x2 = 80000

Factor a perfect square on the left side:
(x + 300)(x + 300) = 80000

Calculate the square root of the right side: 282.842712475

Break this problem into two subproblems by setting 
(x + 300) equal to 282.842712475 and -282.842712475.

Subproblem 1

x + 300 = 282.842712475 Simplifying x + 300 = 282.842712475 Reorder the terms: 300 + x = 282.842712475 Solving 300 + x = 282.842712475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + x = 282.842712475 + -300 Combine like terms: 300 + -300 = 0 0 + x = 282.842712475 + -300 x = 282.842712475 + -300 Combine like terms: 282.842712475 + -300 = -17.157287525 x = -17.157287525 Simplifying x = -17.157287525

Subproblem 2

x + 300 = -282.842712475 Simplifying x + 300 = -282.842712475 Reorder the terms: 300 + x = -282.842712475 Solving 300 + x = -282.842712475 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-300' to each side of the equation. 300 + -300 + x = -282.842712475 + -300 Combine like terms: 300 + -300 = 0 0 + x = -282.842712475 + -300 x = -282.842712475 + -300 Combine like terms: -282.842712475 + -300 = -582.842712475 x = -582.842712475 Simplifying x = -582.842712475

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-17.157287525, -582.842712475}

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