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Simplifying 8x + 5x2 = 10000 Solving 8x + 5x2 = 10000 Solving for variable 'x'. Reorder the terms: -10000 + 8x + 5x2 = 10000 + -10000 Combine like terms: 10000 + -10000 = 0 -10000 + 8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2000 + 1.6x + x2 = 0 Move the constant term to the right: Add '2000' to each side of the equation. -2000 + 1.6x + 2000 + x2 = 0 + 2000 Reorder the terms: -2000 + 2000 + 1.6x + x2 = 0 + 2000 Combine like terms: -2000 + 2000 = 0 0 + 1.6x + x2 = 0 + 2000 1.6x + x2 = 0 + 2000 Combine like terms: 0 + 2000 = 2000 1.6x + x2 = 2000 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 2000 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 2000 + 0.64 Combine like terms: 2000 + 0.64 = 2000.64 0.64 + 1.6x + x2 = 2000.64 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 2000.64 Calculate the square root of the right side: 44.728514395 Break this problem into two subproblems by setting (x + 0.8) equal to 44.728514395 and -44.728514395.Subproblem 1
x + 0.8 = 44.728514395 Simplifying x + 0.8 = 44.728514395 Reorder the terms: 0.8 + x = 44.728514395 Solving 0.8 + x = 44.728514395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 44.728514395 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 44.728514395 + -0.8 x = 44.728514395 + -0.8 Combine like terms: 44.728514395 + -0.8 = 43.928514395 x = 43.928514395 Simplifying x = 43.928514395Subproblem 2
x + 0.8 = -44.728514395 Simplifying x + 0.8 = -44.728514395 Reorder the terms: 0.8 + x = -44.728514395 Solving 0.8 + x = -44.728514395 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -44.728514395 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -44.728514395 + -0.8 x = -44.728514395 + -0.8 Combine like terms: -44.728514395 + -0.8 = -45.528514395 x = -45.528514395 Simplifying x = -45.528514395Solution
The solution to the problem is based on the solutions from the subproblems. x = {43.928514395, -45.528514395}
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