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Simplifying x2 + 5x + -320 = 0 Reorder the terms: -320 + 5x + x2 = 0 Solving -320 + 5x + 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 + 5x + 320 + x2 = 0 + 320 Reorder the terms: -320 + 320 + 5x + x2 = 0 + 320 Combine like terms: -320 + 320 = 0 0 + 5x + x2 = 0 + 320 5x + x2 = 0 + 320 Combine like terms: 0 + 320 = 320 5x + x2 = 320 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 320 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 320 + 6.25 Combine like terms: 320 + 6.25 = 326.25 6.25 + 5x + x2 = 326.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 326.25 Calculate the square root of the right side: 18.062391868 Break this problem into two subproblems by setting (x + 2.5) equal to 18.062391868 and -18.062391868.Subproblem 1
x + 2.5 = 18.062391868 Simplifying x + 2.5 = 18.062391868 Reorder the terms: 2.5 + x = 18.062391868 Solving 2.5 + x = 18.062391868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 18.062391868 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 18.062391868 + -2.5 x = 18.062391868 + -2.5 Combine like terms: 18.062391868 + -2.5 = 15.562391868 x = 15.562391868 Simplifying x = 15.562391868Subproblem 2
x + 2.5 = -18.062391868 Simplifying x + 2.5 = -18.062391868 Reorder the terms: 2.5 + x = -18.062391868 Solving 2.5 + x = -18.062391868 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -18.062391868 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -18.062391868 + -2.5 x = -18.062391868 + -2.5 Combine like terms: -18.062391868 + -2.5 = -20.562391868 x = -20.562391868 Simplifying x = -20.562391868Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.562391868, -20.562391868}
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