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Simplifying (x2) + 30x + -40 = 0 x2 + 30x + -40 = 0 Reorder the terms: -40 + 30x + x2 = 0 Solving -40 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + 30x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 30x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 30x + x2 = 0 + 40 30x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 30x + x2 = 40 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = 40 + 225 Reorder the terms: 225 + 30x + x2 = 40 + 225 Combine like terms: 40 + 225 = 265 225 + 30x + x2 = 265 Factor a perfect square on the left side: (x + 15)(x + 15) = 265 Calculate the square root of the right side: 16.278820596 Break this problem into two subproblems by setting (x + 15) equal to 16.278820596 and -16.278820596.Subproblem 1
x + 15 = 16.278820596 Simplifying x + 15 = 16.278820596 Reorder the terms: 15 + x = 16.278820596 Solving 15 + x = 16.278820596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 16.278820596 + -15 Combine like terms: 15 + -15 = 0 0 + x = 16.278820596 + -15 x = 16.278820596 + -15 Combine like terms: 16.278820596 + -15 = 1.278820596 x = 1.278820596 Simplifying x = 1.278820596Subproblem 2
x + 15 = -16.278820596 Simplifying x + 15 = -16.278820596 Reorder the terms: 15 + x = -16.278820596 Solving 15 + x = -16.278820596 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -16.278820596 + -15 Combine like terms: 15 + -15 = 0 0 + x = -16.278820596 + -15 x = -16.278820596 + -15 Combine like terms: -16.278820596 + -15 = -31.278820596 x = -31.278820596 Simplifying x = -31.278820596Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.278820596, -31.278820596}
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