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Simplifying x2 + 37x + 53 = 0 Reorder the terms: 53 + 37x + x2 = 0 Solving 53 + 37x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-53' to each side of the equation. 53 + 37x + -53 + x2 = 0 + -53 Reorder the terms: 53 + -53 + 37x + x2 = 0 + -53 Combine like terms: 53 + -53 = 0 0 + 37x + x2 = 0 + -53 37x + x2 = 0 + -53 Combine like terms: 0 + -53 = -53 37x + x2 = -53 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 = -53 + 342.25 Reorder the terms: 342.25 + 37x + x2 = -53 + 342.25 Combine like terms: -53 + 342.25 = 289.25 342.25 + 37x + x2 = 289.25 Factor a perfect square on the left side: (x + 18.5)(x + 18.5) = 289.25 Calculate the square root of the right side: 17.007351352 Break this problem into two subproblems by setting (x + 18.5) equal to 17.007351352 and -17.007351352.Subproblem 1
x + 18.5 = 17.007351352 Simplifying x + 18.5 = 17.007351352 Reorder the terms: 18.5 + x = 17.007351352 Solving 18.5 + x = 17.007351352 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 = 17.007351352 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = 17.007351352 + -18.5 x = 17.007351352 + -18.5 Combine like terms: 17.007351352 + -18.5 = -1.492648648 x = -1.492648648 Simplifying x = -1.492648648Subproblem 2
x + 18.5 = -17.007351352 Simplifying x + 18.5 = -17.007351352 Reorder the terms: 18.5 + x = -17.007351352 Solving 18.5 + x = -17.007351352 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 = -17.007351352 + -18.5 Combine like terms: 18.5 + -18.5 = 0.0 0.0 + x = -17.007351352 + -18.5 x = -17.007351352 + -18.5 Combine like terms: -17.007351352 + -18.5 = -35.507351352 x = -35.507351352 Simplifying x = -35.507351352Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.492648648, -35.507351352}
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