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Simplifying 600 + -60x + x2 = 0 Solving 600 + -60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-600' to each side of the equation. 600 + -60x + -600 + x2 = 0 + -600 Reorder the terms: 600 + -600 + -60x + x2 = 0 + -600 Combine like terms: 600 + -600 = 0 0 + -60x + x2 = 0 + -600 -60x + x2 = 0 + -600 Combine like terms: 0 + -600 = -600 -60x + x2 = -600 The x term is -60x. Take half its coefficient (-30). Square it (900) and add it to both sides. Add '900' to each side of the equation. -60x + 900 + x2 = -600 + 900 Reorder the terms: 900 + -60x + x2 = -600 + 900 Combine like terms: -600 + 900 = 300 900 + -60x + x2 = 300 Factor a perfect square on the left side: (x + -30)(x + -30) = 300 Calculate the square root of the right side: 17.320508076 Break this problem into two subproblems by setting (x + -30) equal to 17.320508076 and -17.320508076.Subproblem 1
x + -30 = 17.320508076 Simplifying x + -30 = 17.320508076 Reorder the terms: -30 + x = 17.320508076 Solving -30 + x = 17.320508076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = 17.320508076 + 30 Combine like terms: -30 + 30 = 0 0 + x = 17.320508076 + 30 x = 17.320508076 + 30 Combine like terms: 17.320508076 + 30 = 47.320508076 x = 47.320508076 Simplifying x = 47.320508076Subproblem 2
x + -30 = -17.320508076 Simplifying x + -30 = -17.320508076 Reorder the terms: -30 + x = -17.320508076 Solving -30 + x = -17.320508076 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '30' to each side of the equation. -30 + 30 + x = -17.320508076 + 30 Combine like terms: -30 + 30 = 0 0 + x = -17.320508076 + 30 x = -17.320508076 + 30 Combine like terms: -17.320508076 + 30 = 12.679491924 x = 12.679491924 Simplifying x = 12.679491924Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.320508076, 12.679491924}
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