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Simplifying x2 + -30x + 60 = 0 Reorder the terms: 60 + -30x + x2 = 0 Solving 60 + -30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-60' to each side of the equation. 60 + -30x + -60 + x2 = 0 + -60 Reorder the terms: 60 + -60 + -30x + x2 = 0 + -60 Combine like terms: 60 + -60 = 0 0 + -30x + x2 = 0 + -60 -30x + x2 = 0 + -60 Combine like terms: 0 + -60 = -60 -30x + x2 = -60 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 = -60 + 225 Reorder the terms: 225 + -30x + x2 = -60 + 225 Combine like terms: -60 + 225 = 165 225 + -30x + x2 = 165 Factor a perfect square on the left side: (x + -15)(x + -15) = 165 Calculate the square root of the right side: 12.845232579 Break this problem into two subproblems by setting (x + -15) equal to 12.845232579 and -12.845232579.Subproblem 1
x + -15 = 12.845232579 Simplifying x + -15 = 12.845232579 Reorder the terms: -15 + x = 12.845232579 Solving -15 + x = 12.845232579 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 = 12.845232579 + 15 Combine like terms: -15 + 15 = 0 0 + x = 12.845232579 + 15 x = 12.845232579 + 15 Combine like terms: 12.845232579 + 15 = 27.845232579 x = 27.845232579 Simplifying x = 27.845232579Subproblem 2
x + -15 = -12.845232579 Simplifying x + -15 = -12.845232579 Reorder the terms: -15 + x = -12.845232579 Solving -15 + x = -12.845232579 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 = -12.845232579 + 15 Combine like terms: -15 + 15 = 0 0 + x = -12.845232579 + 15 x = -12.845232579 + 15 Combine like terms: -12.845232579 + 15 = 2.154767421 x = 2.154767421 Simplifying x = 2.154767421Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.845232579, 2.154767421}
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