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Simplifying x2 + 40x + -60 = 0 Reorder the terms: -60 + 40x + x2 = 0 Solving -60 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 40x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 40x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 40x + x2 = 0 + 60 40x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 40x + x2 = 60 The x term is 40x. Take half its coefficient (20). Square it (400) and add it to both sides. Add '400' to each side of the equation. 40x + 400 + x2 = 60 + 400 Reorder the terms: 400 + 40x + x2 = 60 + 400 Combine like terms: 60 + 400 = 460 400 + 40x + x2 = 460 Factor a perfect square on the left side: (x + 20)(x + 20) = 460 Calculate the square root of the right side: 21.44761059 Break this problem into two subproblems by setting (x + 20) equal to 21.44761059 and -21.44761059.Subproblem 1
x + 20 = 21.44761059 Simplifying x + 20 = 21.44761059 Reorder the terms: 20 + x = 21.44761059 Solving 20 + x = 21.44761059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = 21.44761059 + -20 Combine like terms: 20 + -20 = 0 0 + x = 21.44761059 + -20 x = 21.44761059 + -20 Combine like terms: 21.44761059 + -20 = 1.44761059 x = 1.44761059 Simplifying x = 1.44761059Subproblem 2
x + 20 = -21.44761059 Simplifying x + 20 = -21.44761059 Reorder the terms: 20 + x = -21.44761059 Solving 20 + x = -21.44761059 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + x = -21.44761059 + -20 Combine like terms: 20 + -20 = 0 0 + x = -21.44761059 + -20 x = -21.44761059 + -20 Combine like terms: -21.44761059 + -20 = -41.44761059 x = -41.44761059 Simplifying x = -41.44761059Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.44761059, -41.44761059}
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