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Simplifying x2 + 36x + 303 = 0 Reorder the terms: 303 + 36x + x2 = 0 Solving 303 + 36x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-303' to each side of the equation. 303 + 36x + -303 + x2 = 0 + -303 Reorder the terms: 303 + -303 + 36x + x2 = 0 + -303 Combine like terms: 303 + -303 = 0 0 + 36x + x2 = 0 + -303 36x + x2 = 0 + -303 Combine like terms: 0 + -303 = -303 36x + x2 = -303 The x term is 36x. Take half its coefficient (18). Square it (324) and add it to both sides. Add '324' to each side of the equation. 36x + 324 + x2 = -303 + 324 Reorder the terms: 324 + 36x + x2 = -303 + 324 Combine like terms: -303 + 324 = 21 324 + 36x + x2 = 21 Factor a perfect square on the left side: (x + 18)(x + 18) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (x + 18) equal to 4.582575695 and -4.582575695.Subproblem 1
x + 18 = 4.582575695 Simplifying x + 18 = 4.582575695 Reorder the terms: 18 + x = 4.582575695 Solving 18 + x = 4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = 4.582575695 + -18 Combine like terms: 18 + -18 = 0 0 + x = 4.582575695 + -18 x = 4.582575695 + -18 Combine like terms: 4.582575695 + -18 = -13.417424305 x = -13.417424305 Simplifying x = -13.417424305Subproblem 2
x + 18 = -4.582575695 Simplifying x + 18 = -4.582575695 Reorder the terms: 18 + x = -4.582575695 Solving 18 + x = -4.582575695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + x = -4.582575695 + -18 Combine like terms: 18 + -18 = 0 0 + x = -4.582575695 + -18 x = -4.582575695 + -18 Combine like terms: -4.582575695 + -18 = -22.582575695 x = -22.582575695 Simplifying x = -22.582575695Solution
The solution to the problem is based on the solutions from the subproblems. x = {-13.417424305, -22.582575695}
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