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Simplifying x2 + 37x + 59 = 0 Reorder the terms: 59 + 37x + x2 = 0 Solving 59 + 37x + 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 + 37x + -59 + x2 = 0 + -59 Reorder the terms: 59 + -59 + 37x + x2 = 0 + -59 Combine like terms: 59 + -59 = 0 0 + 37x + x2 = 0 + -59 37x + x2 = 0 + -59 Combine like terms: 0 + -59 = -59 37x + x2 = -59 The x term is 37x. Take half its coefficient (18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. 37x + 342.25 + x2 = -59 + 342.25 Reorder the terms: 342.25 + 37x + x2 = -59 + 342.25 Combine like terms: -59 + 342.25 = 283.25 342.25 + 37x + x2 = 283.25 Factor a perfect square on the left side: (x + 18.5)(x + 18.5) = 283.25 Calculate the square root of the right side: 16.83003268 Break this problem into two subproblems by setting (x + 18.5) equal to 16.83003268 and -16.83003268.Subproblem 1
x + 18.5 = 16.83003268 Simplifying x + 18.5 = 16.83003268 Reorder the terms: 18.5 + x = 16.83003268 Solving 18.5 + x = 16.83003268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + x = 16.83003268 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = 16.83003268 + -18.5 x = 16.83003268 + -18.5 Combine like terms: 16.83003268 + -18.5 = -1.66996732 x = -1.66996732 Simplifying x = -1.66996732Subproblem 2
x + 18.5 = -16.83003268 Simplifying x + 18.5 = -16.83003268 Reorder the terms: 18.5 + x = -16.83003268 Solving 18.5 + x = -16.83003268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18.5' to each side of the equation. 18.5 + -18.5 + x = -16.83003268 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = -16.83003268 + -18.5 x = -16.83003268 + -18.5 Combine like terms: -16.83003268 + -18.5 = -35.33003268 x = -35.33003268 Simplifying x = -35.33003268Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.66996732, -35.33003268}
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