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Simplifying x2 + 6x + -35 = 180 Reorder the terms: -35 + 6x + x2 = 180 Solving -35 + 6x + x2 = 180 Solving for variable 'x'. Reorder the terms: -35 + -180 + 6x + x2 = 180 + -180 Combine like terms: -35 + -180 = -215 -215 + 6x + x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -215 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '215' to each side of the equation. -215 + 6x + 215 + x2 = 0 + 215 Reorder the terms: -215 + 215 + 6x + x2 = 0 + 215 Combine like terms: -215 + 215 = 0 0 + 6x + x2 = 0 + 215 6x + x2 = 0 + 215 Combine like terms: 0 + 215 = 215 6x + x2 = 215 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 215 + 9 Reorder the terms: 9 + 6x + x2 = 215 + 9 Combine like terms: 215 + 9 = 224 9 + 6x + x2 = 224 Factor a perfect square on the left side: (x + 3)(x + 3) = 224 Calculate the square root of the right side: 14.966629547 Break this problem into two subproblems by setting (x + 3) equal to 14.966629547 and -14.966629547.Subproblem 1
x + 3 = 14.966629547 Simplifying x + 3 = 14.966629547 Reorder the terms: 3 + x = 14.966629547 Solving 3 + x = 14.966629547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 14.966629547 + -3 Combine like terms: 3 + -3 = 0 0 + x = 14.966629547 + -3 x = 14.966629547 + -3 Combine like terms: 14.966629547 + -3 = 11.966629547 x = 11.966629547 Simplifying x = 11.966629547Subproblem 2
x + 3 = -14.966629547 Simplifying x + 3 = -14.966629547 Reorder the terms: 3 + x = -14.966629547 Solving 3 + x = -14.966629547 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -14.966629547 + -3 Combine like terms: 3 + -3 = 0 0 + x = -14.966629547 + -3 x = -14.966629547 + -3 Combine like terms: -14.966629547 + -3 = -17.966629547 x = -17.966629547 Simplifying x = -17.966629547Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.966629547, -17.966629547}
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