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Simplifying 40x2 + x + -4000 = 0 Reorder the terms: -4000 + x + 40x2 = 0 Solving -4000 + x + 40x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -100 + 0.025x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + 0.025x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + 0.025x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 0.025x + x2 = 0 + 100 0.025x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 0.025x + x2 = 100 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. 0.025x + 0.25 + x2 = 100 + 0.25 Reorder the terms: 0.25 + 0.025x + x2 = 100 + 0.25 Combine like terms: 100 + 0.25 = 100.25 0.25 + 0.025x + x2 = 100.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (x + 0.5) equal to 10.012492197 and -10.012492197.Subproblem 1
x + 0.5 = 10.012492197 Simplifying x + 0.5 = 10.012492197 Reorder the terms: 0.5 + x = 10.012492197 Solving 0.5 + x = 10.012492197 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 = 10.012492197 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 10.012492197 + -0.5 x = 10.012492197 + -0.5 Combine like terms: 10.012492197 + -0.5 = 9.512492197 x = 9.512492197 Simplifying x = 9.512492197Subproblem 2
x + 0.5 = -10.012492197 Simplifying x + 0.5 = -10.012492197 Reorder the terms: 0.5 + x = -10.012492197 Solving 0.5 + x = -10.012492197 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 = -10.012492197 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -10.012492197 + -0.5 x = -10.012492197 + -0.5 Combine like terms: -10.012492197 + -0.5 = -10.512492197 x = -10.512492197 Simplifying x = -10.512492197Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.512492197, -10.512492197}
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