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Simplifying 4x2 + x + -360000 = 0 Reorder the terms: -360000 + x + 4x2 = 0 Solving -360000 + x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -90000 + 0.25x + x2 = 0 Move the constant term to the right: Add '90000' to each side of the equation. -90000 + 0.25x + 90000 + x2 = 0 + 90000 Reorder the terms: -90000 + 90000 + 0.25x + x2 = 0 + 90000 Combine like terms: -90000 + 90000 = 0 0 + 0.25x + x2 = 0 + 90000 0.25x + x2 = 0 + 90000 Combine like terms: 0 + 90000 = 90000 0.25x + x2 = 90000 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. 0.25x + 0.25 + x2 = 90000 + 0.25 Reorder the terms: 0.25 + 0.25x + x2 = 90000 + 0.25 Combine like terms: 90000 + 0.25 = 90000.25 0.25 + 0.25x + x2 = 90000.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 90000.25 Calculate the square root of the right side: 300.000416666 Break this problem into two subproblems by setting (x + 0.5) equal to 300.000416666 and -300.000416666.Subproblem 1
x + 0.5 = 300.000416666 Simplifying x + 0.5 = 300.000416666 Reorder the terms: 0.5 + x = 300.000416666 Solving 0.5 + x = 300.000416666 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 = 300.000416666 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 300.000416666 + -0.5 x = 300.000416666 + -0.5 Combine like terms: 300.000416666 + -0.5 = 299.500416666 x = 299.500416666 Simplifying x = 299.500416666Subproblem 2
x + 0.5 = -300.000416666 Simplifying x + 0.5 = -300.000416666 Reorder the terms: 0.5 + x = -300.000416666 Solving 0.5 + x = -300.000416666 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 = -300.000416666 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -300.000416666 + -0.5 x = -300.000416666 + -0.5 Combine like terms: -300.000416666 + -0.5 = -300.500416666 x = -300.500416666 Simplifying x = -300.500416666Solution
The solution to the problem is based on the solutions from the subproblems. x = {299.500416666, -300.500416666}
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