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Simplifying (x2) + 0.75x = 800 x2 + 0.75x = 800 Reorder the terms: 0.75x + x2 = 800 Solving 0.75x + x2 = 800 Solving for variable 'x'. Reorder the terms: -800 + 0.75x + x2 = 800 + -800 Combine like terms: 800 + -800 = 0 -800 + 0.75x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '800' to each side of the equation. -800 + 0.75x + 800 + x2 = 0 + 800 Reorder the terms: -800 + 800 + 0.75x + x2 = 0 + 800 Combine like terms: -800 + 800 = 0 0 + 0.75x + x2 = 0 + 800 0.75x + x2 = 0 + 800 Combine like terms: 0 + 800 = 800 0.75x + x2 = 800 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 800 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 800 + 0.140625 Combine like terms: 800 + 0.140625 = 800.140625 0.140625 + 0.75x + x2 = 800.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 800.140625 Calculate the square root of the right side: 28.286757061 Break this problem into two subproblems by setting (x + 0.375) equal to 28.286757061 and -28.286757061.Subproblem 1
x + 0.375 = 28.286757061 Simplifying x + 0.375 = 28.286757061 Reorder the terms: 0.375 + x = 28.286757061 Solving 0.375 + x = 28.286757061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 28.286757061 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 28.286757061 + -0.375 x = 28.286757061 + -0.375 Combine like terms: 28.286757061 + -0.375 = 27.911757061 x = 27.911757061 Simplifying x = 27.911757061Subproblem 2
x + 0.375 = -28.286757061 Simplifying x + 0.375 = -28.286757061 Reorder the terms: 0.375 + x = -28.286757061 Solving 0.375 + x = -28.286757061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -28.286757061 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -28.286757061 + -0.375 x = -28.286757061 + -0.375 Combine like terms: -28.286757061 + -0.375 = -28.661757061 x = -28.661757061 Simplifying x = -28.661757061Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.911757061, -28.661757061}
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