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Simplifying x2 + x + -320 = 0 Reorder the terms: -320 + x + x2 = 0 Solving -320 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '320' to each side of the equation. -320 + x + 320 + x2 = 0 + 320 Reorder the terms: -320 + 320 + x + x2 = 0 + 320 Combine like terms: -320 + 320 = 0 0 + x + x2 = 0 + 320 x + x2 = 0 + 320 Combine like terms: 0 + 320 = 320 x + x2 = 320 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. x + 0.25 + x2 = 320 + 0.25 Reorder the terms: 0.25 + x + x2 = 320 + 0.25 Combine like terms: 320 + 0.25 = 320.25 0.25 + x + x2 = 320.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 320.25 Calculate the square root of the right side: 17.895530168 Break this problem into two subproblems by setting (x + 0.5) equal to 17.895530168 and -17.895530168.Subproblem 1
x + 0.5 = 17.895530168 Simplifying x + 0.5 = 17.895530168 Reorder the terms: 0.5 + x = 17.895530168 Solving 0.5 + x = 17.895530168 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 = 17.895530168 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 17.895530168 + -0.5 x = 17.895530168 + -0.5 Combine like terms: 17.895530168 + -0.5 = 17.395530168 x = 17.395530168 Simplifying x = 17.395530168Subproblem 2
x + 0.5 = -17.895530168 Simplifying x + 0.5 = -17.895530168 Reorder the terms: 0.5 + x = -17.895530168 Solving 0.5 + x = -17.895530168 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 = -17.895530168 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -17.895530168 + -0.5 x = -17.895530168 + -0.5 Combine like terms: -17.895530168 + -0.5 = -18.395530168 x = -18.395530168 Simplifying x = -18.395530168Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.395530168, -18.395530168}
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