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Simplifying x2 + 40x + 59 = 0 Reorder the terms: 59 + 40x + x2 = 0 Solving 59 + 40x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-59' to each side of the equation. 59 + 40x + -59 + x2 = 0 + -59 Reorder the terms: 59 + -59 + 40x + x2 = 0 + -59 Combine like terms: 59 + -59 = 0 0 + 40x + x2 = 0 + -59 40x + x2 = 0 + -59 Combine like terms: 0 + -59 = -59 40x + x2 = -59 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 = -59 + 400 Reorder the terms: 400 + 40x + x2 = -59 + 400 Combine like terms: -59 + 400 = 341 400 + 40x + x2 = 341 Factor a perfect square on the left side: (x + 20)(x + 20) = 341 Calculate the square root of the right side: 18.466185313 Break this problem into two subproblems by setting (x + 20) equal to 18.466185313 and -18.466185313.Subproblem 1
x + 20 = 18.466185313 Simplifying x + 20 = 18.466185313 Reorder the terms: 20 + x = 18.466185313 Solving 20 + x = 18.466185313 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 = 18.466185313 + -20 Combine like terms: 20 + -20 = 0 0 + x = 18.466185313 + -20 x = 18.466185313 + -20 Combine like terms: 18.466185313 + -20 = -1.533814687 x = -1.533814687 Simplifying x = -1.533814687Subproblem 2
x + 20 = -18.466185313 Simplifying x + 20 = -18.466185313 Reorder the terms: 20 + x = -18.466185313 Solving 20 + x = -18.466185313 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 = -18.466185313 + -20 Combine like terms: 20 + -20 = 0 0 + x = -18.466185313 + -20 x = -18.466185313 + -20 Combine like terms: -18.466185313 + -20 = -38.466185313 x = -38.466185313 Simplifying x = -38.466185313Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.533814687, -38.466185313}
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