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Simplifying x2 + -30x + -120 = 0 Reorder the terms: -120 + -30x + x2 = 0 Solving -120 + -30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '120' to each side of the equation. -120 + -30x + 120 + x2 = 0 + 120 Reorder the terms: -120 + 120 + -30x + x2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + -30x + x2 = 0 + 120 -30x + x2 = 0 + 120 Combine like terms: 0 + 120 = 120 -30x + x2 = 120 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = 120 + 225 Reorder the terms: 225 + -30x + x2 = 120 + 225 Combine like terms: 120 + 225 = 345 225 + -30x + x2 = 345 Factor a perfect square on the left side: (x + -15)(x + -15) = 345 Calculate the square root of the right side: 18.574175621 Break this problem into two subproblems by setting (x + -15) equal to 18.574175621 and -18.574175621.Subproblem 1
x + -15 = 18.574175621 Simplifying x + -15 = 18.574175621 Reorder the terms: -15 + x = 18.574175621 Solving -15 + x = 18.574175621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 18.574175621 + 15 Combine like terms: -15 + 15 = 0 0 + x = 18.574175621 + 15 x = 18.574175621 + 15 Combine like terms: 18.574175621 + 15 = 33.574175621 x = 33.574175621 Simplifying x = 33.574175621Subproblem 2
x + -15 = -18.574175621 Simplifying x + -15 = -18.574175621 Reorder the terms: -15 + x = -18.574175621 Solving -15 + x = -18.574175621 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -18.574175621 + 15 Combine like terms: -15 + 15 = 0 0 + x = -18.574175621 + 15 x = -18.574175621 + 15 Combine like terms: -18.574175621 + 15 = -3.574175621 x = -3.574175621 Simplifying x = -3.574175621Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.574175621, -3.574175621}
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