-0.2x^2+26x+280=1000

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Solution for -0.2x^2+26x+280=1000 equation:


Simplifying
-0.2x2 + 26x + 280 = 1000

Reorder the terms:
280 + 26x + -0.2x2 = 1000

Solving
280 + 26x + -0.2x2 = 1000

Solving for variable 'x'.

Reorder the terms:
280 + -1000 + 26x + -0.2x2 = 1000 + -1000

Combine like terms: 280 + -1000 = -720
-720 + 26x + -0.2x2 = 1000 + -1000

Combine like terms: 1000 + -1000 = 0
-720 + 26x + -0.2x2 = 0

Begin completing the square.  Divide all terms by
-0.2 the coefficient of the squared term: 

Divide each side by '-0.2'.
3600 + -130x + x2 = 0

Move the constant term to the right:

Add '-3600' to each side of the equation.
3600 + -130x + -3600 + x2 = 0 + -3600

Reorder the terms:
3600 + -3600 + -130x + x2 = 0 + -3600

Combine like terms: 3600 + -3600 = 0
0 + -130x + x2 = 0 + -3600
-130x + x2 = 0 + -3600

Combine like terms: 0 + -3600 = -3600
-130x + x2 = -3600

The x term is -130x.  Take half its coefficient (-65).
Square it (4225) and add it to both sides.

Add '4225' to each side of the equation.
-130x + 4225 + x2 = -3600 + 4225

Reorder the terms:
4225 + -130x + x2 = -3600 + 4225

Combine like terms: -3600 + 4225 = 625
4225 + -130x + x2 = 625

Factor a perfect square on the left side:
(x + -65)(x + -65) = 625

Calculate the square root of the right side: 25

Break this problem into two subproblems by setting 
(x + -65) equal to 25 and -25.

Subproblem 1

x + -65 = 25 Simplifying x + -65 = 25 Reorder the terms: -65 + x = 25 Solving -65 + x = 25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + x = 25 + 65 Combine like terms: -65 + 65 = 0 0 + x = 25 + 65 x = 25 + 65 Combine like terms: 25 + 65 = 90 x = 90 Simplifying x = 90

Subproblem 2

x + -65 = -25 Simplifying x + -65 = -25 Reorder the terms: -65 + x = -25 Solving -65 + x = -25 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '65' to each side of the equation. -65 + 65 + x = -25 + 65 Combine like terms: -65 + 65 = 0 0 + x = -25 + 65 x = -25 + 65 Combine like terms: -25 + 65 = 40 x = 40 Simplifying x = 40

Solution

The solution to the problem is based on the solutions from the subproblems. x = {90, 40}

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