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Simplifying 0.5x + x2 = 800 Solving 0.5x + x2 = 800 Solving for variable 'x'. Reorder the terms: -800 + 0.5x + x2 = 800 + -800 Combine like terms: 800 + -800 = 0 -800 + 0.5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '800' to each side of the equation. -800 + 0.5x + 800 + x2 = 0 + 800 Reorder the terms: -800 + 800 + 0.5x + x2 = 0 + 800 Combine like terms: -800 + 800 = 0 0 + 0.5x + x2 = 0 + 800 0.5x + x2 = 0 + 800 Combine like terms: 0 + 800 = 800 0.5x + x2 = 800 The x term is 0.5x. Take half its coefficient (0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. 0.5x + 0.0625 + x2 = 800 + 0.0625 Reorder the terms: 0.0625 + 0.5x + x2 = 800 + 0.0625 Combine like terms: 800 + 0.0625 = 800.0625 0.0625 + 0.5x + x2 = 800.0625 Factor a perfect square on the left side: (x + 0.25)(x + 0.25) = 800.0625 Calculate the square root of the right side: 28.28537608 Break this problem into two subproblems by setting (x + 0.25) equal to 28.28537608 and -28.28537608.Subproblem 1
x + 0.25 = 28.28537608 Simplifying x + 0.25 = 28.28537608 Reorder the terms: 0.25 + x = 28.28537608 Solving 0.25 + x = 28.28537608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = 28.28537608 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = 28.28537608 + -0.25 x = 28.28537608 + -0.25 Combine like terms: 28.28537608 + -0.25 = 28.03537608 x = 28.03537608 Simplifying x = 28.03537608Subproblem 2
x + 0.25 = -28.28537608 Simplifying x + 0.25 = -28.28537608 Reorder the terms: 0.25 + x = -28.28537608 Solving 0.25 + x = -28.28537608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.25' to each side of the equation. 0.25 + -0.25 + x = -28.28537608 + -0.25 Combine like terms: 0.25 + -0.25 = 0.00 0.00 + x = -28.28537608 + -0.25 x = -28.28537608 + -0.25 Combine like terms: -28.28537608 + -0.25 = -28.53537608 x = -28.53537608 Simplifying x = -28.53537608Solution
The solution to the problem is based on the solutions from the subproblems. x = {28.03537608, -28.53537608}
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