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Simplifying 800 + -1x2 + -1x = 0 Reorder the terms: 800 + -1x + -1x2 = 0 Solving 800 + -1x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -800 + x + x2 = 0 Move the constant term to the right: Add '800' to each side of the equation. -800 + x + 800 + x2 = 0 + 800 Reorder the terms: -800 + 800 + x + x2 = 0 + 800 Combine like terms: -800 + 800 = 0 0 + x + x2 = 0 + 800 x + x2 = 0 + 800 Combine like terms: 0 + 800 = 800 x + x2 = 800 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. + 0.25 + x2 = 800 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 800 + 0.25 Combine like terms: 800 + 0.25 = 800.25 1.25 + x2 = 800.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 800.25 Calculate the square root of the right side: 28.28869032 Break this problem into two subproblems by setting (x + 0.5) equal to 28.28869032 and -28.28869032.Subproblem 1
x + 0.5 = 28.28869032 Simplifying x + 0.5 = 28.28869032 Reorder the terms: 0.5 + x = 28.28869032 Solving 0.5 + x = 28.28869032 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 = 28.28869032 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 28.28869032 + -0.5 x = 28.28869032 + -0.5 Combine like terms: 28.28869032 + -0.5 = 27.78869032 x = 27.78869032 Simplifying x = 27.78869032Subproblem 2
x + 0.5 = -28.28869032 Simplifying x + 0.5 = -28.28869032 Reorder the terms: 0.5 + x = -28.28869032 Solving 0.5 + x = -28.28869032 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 = -28.28869032 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -28.28869032 + -0.5 x = -28.28869032 + -0.5 Combine like terms: -28.28869032 + -0.5 = -28.78869032 x = -28.78869032 Simplifying x = -28.78869032Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.78869032, -28.78869032}
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