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Simplifying x2 + 35x + 3 = 0 Reorder the terms: 3 + 35x + x2 = 0 Solving 3 + 35x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + 35x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + 35x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + 35x + x2 = 0 + -3 35x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 35x + x2 = -3 The x term is 35x. Take half its coefficient (17.5). Square it (306.25) and add it to both sides. Add '306.25' to each side of the equation. 35x + 306.25 + x2 = -3 + 306.25 Reorder the terms: 306.25 + 35x + x2 = -3 + 306.25 Combine like terms: -3 + 306.25 = 303.25 306.25 + 35x + x2 = 303.25 Factor a perfect square on the left side: (x + 17.5)(x + 17.5) = 303.25 Calculate the square root of the right side: 17.414074767 Break this problem into two subproblems by setting (x + 17.5) equal to 17.414074767 and -17.414074767.Subproblem 1
x + 17.5 = 17.414074767 Simplifying x + 17.5 = 17.414074767 Reorder the terms: 17.5 + x = 17.414074767 Solving 17.5 + x = 17.414074767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = 17.414074767 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = 17.414074767 + -17.5 x = 17.414074767 + -17.5 Combine like terms: 17.414074767 + -17.5 = -0.085925233 x = -0.085925233 Simplifying x = -0.085925233Subproblem 2
x + 17.5 = -17.414074767 Simplifying x + 17.5 = -17.414074767 Reorder the terms: 17.5 + x = -17.414074767 Solving 17.5 + x = -17.414074767 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.5' to each side of the equation. 17.5 + -17.5 + x = -17.414074767 + -17.5 Combine like terms: 17.5 + -17.5 = 0.0 0.0 + x = -17.414074767 + -17.5 x = -17.414074767 + -17.5 Combine like terms: -17.414074767 + -17.5 = -34.914074767 x = -34.914074767 Simplifying x = -34.914074767Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.085925233, -34.914074767}
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