-x^2+100x=1000

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Solution for -x^2+100x=1000 equation:


Simplifying
-1x2 + 100x = 1000

Reorder the terms:
100x + -1x2 = 1000

Solving
100x + -1x2 = 1000

Solving for variable 'x'.

Reorder the terms:
-1000 + 100x + -1x2 = 1000 + -1000

Combine like terms: 1000 + -1000 = 0
-1000 + 100x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
1000 + -100x + x2 = 0

Move the constant term to the right:

Add '-1000' to each side of the equation.
1000 + -100x + -1000 + x2 = 0 + -1000

Reorder the terms:
1000 + -1000 + -100x + x2 = 0 + -1000

Combine like terms: 1000 + -1000 = 0
0 + -100x + x2 = 0 + -1000
-100x + x2 = 0 + -1000

Combine like terms: 0 + -1000 = -1000
-100x + x2 = -1000

The x term is -100x.  Take half its coefficient (-50).
Square it (2500) and add it to both sides.

Add '2500' to each side of the equation.
-100x + 2500 + x2 = -1000 + 2500

Reorder the terms:
2500 + -100x + x2 = -1000 + 2500

Combine like terms: -1000 + 2500 = 1500
2500 + -100x + x2 = 1500

Factor a perfect square on the left side:
(x + -50)(x + -50) = 1500

Calculate the square root of the right side: 38.729833462

Break this problem into two subproblems by setting 
(x + -50) equal to 38.729833462 and -38.729833462.

Subproblem 1

x + -50 = 38.729833462 Simplifying x + -50 = 38.729833462 Reorder the terms: -50 + x = 38.729833462 Solving -50 + x = 38.729833462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 38.729833462 + 50 Combine like terms: -50 + 50 = 0 0 + x = 38.729833462 + 50 x = 38.729833462 + 50 Combine like terms: 38.729833462 + 50 = 88.729833462 x = 88.729833462 Simplifying x = 88.729833462

Subproblem 2

x + -50 = -38.729833462 Simplifying x + -50 = -38.729833462 Reorder the terms: -50 + x = -38.729833462 Solving -50 + x = -38.729833462 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -38.729833462 + 50 Combine like terms: -50 + 50 = 0 0 + x = -38.729833462 + 50 x = -38.729833462 + 50 Combine like terms: -38.729833462 + 50 = 11.270166538 x = 11.270166538 Simplifying x = 11.270166538

Solution

The solution to the problem is based on the solutions from the subproblems. x = {88.729833462, 11.270166538}

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