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Simplifying 0 = 400 + -5x + 0.125x * 0.125x Reorder the terms for easier multiplication: 0 = 400 + -5x + 0.125 * 0.125x * x Multiply 0.125 * 0.125 0 = 400 + -5x + 0.015625x * x Multiply x * x 0 = 400 + -5x + 0.015625x2 Solving 0 = 400 + -5x + 0.015625x2 Solving for variable 'x'. Combine like terms: 0 + -400 = -400 -400 + 5x + -0.015625x2 = 400 + -5x + 0.015625x2 + -400 + 5x + -0.015625x2 Reorder the terms: -400 + 5x + -0.015625x2 = 400 + -400 + -5x + 5x + 0.015625x2 + -0.015625x2 Combine like terms: 400 + -400 = 0 -400 + 5x + -0.015625x2 = 0 + -5x + 5x + 0.015625x2 + -0.015625x2 -400 + 5x + -0.015625x2 = -5x + 5x + 0.015625x2 + -0.015625x2 Combine like terms: -5x + 5x = 0 -400 + 5x + -0.015625x2 = 0 + 0.015625x2 + -0.015625x2 -400 + 5x + -0.015625x2 = 0.015625x2 + -0.015625x2 Combine like terms: 0.015625x2 + -0.015625x2 = 0.000000 -400 + 5x + -0.015625x2 = 0.000000 Begin completing the square. Divide all terms by -0.015625 the coefficient of the squared term: Divide each side by '-0.015625'. 25600 + -320x + x2 = 0 Move the constant term to the right: Add '-25600' to each side of the equation. 25600 + -320x + -25600 + x2 = 0 + -25600 Reorder the terms: 25600 + -25600 + -320x + x2 = 0 + -25600 Combine like terms: 25600 + -25600 = 0 0 + -320x + x2 = 0 + -25600 -320x + x2 = 0 + -25600 Combine like terms: 0 + -25600 = -25600 -320x + x2 = -25600 The x term is -320x. Take half its coefficient (-160). Square it (25600) and add it to both sides. Add '25600' to each side of the equation. -320x + 25600 + x2 = -25600 + 25600 Reorder the terms: 25600 + -320x + x2 = -25600 + 25600 Combine like terms: -25600 + 25600 = 0 25600 + -320x + x2 = 0 Factor a perfect square on the left side: (x + -160)(x + -160) = 0 Calculate the square root of the right side: 0 Break this problem into two subproblems by setting (x + -160) equal to 0 and 0.Subproblem 1
x + -160 = 0 Simplifying x + -160 = 0 Reorder the terms: -160 + x = 0 Solving -160 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '160' to each side of the equation. -160 + 160 + x = 0 + 160 Combine like terms: -160 + 160 = 0 0 + x = 0 + 160 x = 0 + 160 Combine like terms: 0 + 160 = 160 x = 160 Simplifying x = 160Subproblem 2
x + -160 = 0 Simplifying x + -160 = 0 Reorder the terms: -160 + x = 0 Solving -160 + x = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '160' to each side of the equation. -160 + 160 + x = 0 + 160 Combine like terms: -160 + 160 = 0 0 + x = 0 + 160 x = 0 + 160 Combine like terms: 0 + 160 = 160 x = 160 Simplifying x = 160Solution
The solution to the problem is based on the solutions from the subproblems. x = {160, 160}
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