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Simplifying -5x2 + 1000x + 5000 = 0 Reorder the terms: 5000 + 1000x + -5x2 = 0 Solving 5000 + 1000x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(1000 + 200x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1000 + 200x + -1x2)' equal to zero and attempt to solve: Simplifying 1000 + 200x + -1x2 = 0 Solving 1000 + 200x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1000 + -200x + x2 = 0 Move the constant term to the right: Add '1000' to each side of the equation. -1000 + -200x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + -200x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + -200x + x2 = 0 + 1000 -200x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 -200x + x2 = 1000 The x term is -200x. Take half its coefficient (-100). Square it (10000) and add it to both sides. Add '10000' to each side of the equation. -200x + 10000 + x2 = 1000 + 10000 Reorder the terms: 10000 + -200x + x2 = 1000 + 10000 Combine like terms: 1000 + 10000 = 11000 10000 + -200x + x2 = 11000 Factor a perfect square on the left side: (x + -100)(x + -100) = 11000 Calculate the square root of the right side: 104.880884817 Break this problem into two subproblems by setting (x + -100) equal to 104.880884817 and -104.880884817.Subproblem 1
x + -100 = 104.880884817 Simplifying x + -100 = 104.880884817 Reorder the terms: -100 + x = 104.880884817 Solving -100 + x = 104.880884817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 104.880884817 + 100 Combine like terms: -100 + 100 = 0 0 + x = 104.880884817 + 100 x = 104.880884817 + 100 Combine like terms: 104.880884817 + 100 = 204.880884817 x = 204.880884817 Simplifying x = 204.880884817Subproblem 2
x + -100 = -104.880884817 Simplifying x + -100 = -104.880884817 Reorder the terms: -100 + x = -104.880884817 Solving -100 + x = -104.880884817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -104.880884817 + 100 Combine like terms: -100 + 100 = 0 0 + x = -104.880884817 + 100 x = -104.880884817 + 100 Combine like terms: -104.880884817 + 100 = -4.880884817 x = -4.880884817 Simplifying x = -4.880884817Solution
The solution to the problem is based on the solutions from the subproblems. x = {204.880884817, -4.880884817}Solution
x = {204.880884817, -4.880884817}
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