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Simplifying 10x2 + 5x + -2000 = 0 Reorder the terms: -2000 + 5x + 10x2 = 0 Solving -2000 + 5x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-400 + x + 2x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-400 + x + 2x2)' equal to zero and attempt to solve: Simplifying -400 + x + 2x2 = 0 Solving -400 + x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -200 + 0.5x + x2 = 0 Move the constant term to the right: Add '200' to each side of the equation. -200 + 0.5x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + 0.5x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 0.5x + x2 = 0 + 200 0.5x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 0.5x + x2 = 200 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. 0.5x + 0.25 + x2 = 200 + 0.25 Reorder the terms: 0.25 + 0.5x + x2 = 200 + 0.25 Combine like terms: 200 + 0.25 = 200.25 0.25 + 0.5x + x2 = 200.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 200.25 Calculate the square root of the right side: 14.150971698 Break this problem into two subproblems by setting (x + 0.5) equal to 14.150971698 and -14.150971698.Subproblem 1
x + 0.5 = 14.150971698 Simplifying x + 0.5 = 14.150971698 Reorder the terms: 0.5 + x = 14.150971698 Solving 0.5 + x = 14.150971698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 14.150971698 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 14.150971698 + -0.5 x = 14.150971698 + -0.5 Combine like terms: 14.150971698 + -0.5 = 13.650971698 x = 13.650971698 Simplifying x = 13.650971698Subproblem 2
x + 0.5 = -14.150971698 Simplifying x + 0.5 = -14.150971698 Reorder the terms: 0.5 + x = -14.150971698 Solving 0.5 + x = -14.150971698 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -14.150971698 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -14.150971698 + -0.5 x = -14.150971698 + -0.5 Combine like terms: -14.150971698 + -0.5 = -14.650971698 x = -14.650971698 Simplifying x = -14.650971698Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.650971698, -14.650971698}Solution
x = {13.650971698, -14.650971698}
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