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Simplifying 40x2 + x = 1000000 Reorder the terms: x + 40x2 = 1000000 Solving x + 40x2 = 1000000 Solving for variable 'x'. Reorder the terms: -1000000 + x + 40x2 = 1000000 + -1000000 Combine like terms: 1000000 + -1000000 = 0 -1000000 + x + 40x2 = 0 Begin completing the square. Divide all terms by 40 the coefficient of the squared term: Divide each side by '40'. -25000 + 0.025x + x2 = 0 Move the constant term to the right: Add '25000' to each side of the equation. -25000 + 0.025x + 25000 + x2 = 0 + 25000 Reorder the terms: -25000 + 25000 + 0.025x + x2 = 0 + 25000 Combine like terms: -25000 + 25000 = 0 0 + 0.025x + x2 = 0 + 25000 0.025x + x2 = 0 + 25000 Combine like terms: 0 + 25000 = 25000 0.025x + x2 = 25000 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 = 25000 + 0.25 Reorder the terms: 0.25 + 0.025x + x2 = 25000 + 0.25 Combine like terms: 25000 + 0.25 = 25000.25 0.25 + 0.025x + x2 = 25000.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 25000.25 Calculate the square root of the right side: 158.114673576 Break this problem into two subproblems by setting (x + 0.5) equal to 158.114673576 and -158.114673576.Subproblem 1
x + 0.5 = 158.114673576 Simplifying x + 0.5 = 158.114673576 Reorder the terms: 0.5 + x = 158.114673576 Solving 0.5 + x = 158.114673576 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 = 158.114673576 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 158.114673576 + -0.5 x = 158.114673576 + -0.5 Combine like terms: 158.114673576 + -0.5 = 157.614673576 x = 157.614673576 Simplifying x = 157.614673576Subproblem 2
x + 0.5 = -158.114673576 Simplifying x + 0.5 = -158.114673576 Reorder the terms: 0.5 + x = -158.114673576 Solving 0.5 + x = -158.114673576 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 = -158.114673576 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -158.114673576 + -0.5 x = -158.114673576 + -0.5 Combine like terms: -158.114673576 + -0.5 = -158.614673576 x = -158.614673576 Simplifying x = -158.614673576Solution
The solution to the problem is based on the solutions from the subproblems. x = {157.614673576, -158.614673576}
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