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Simplifying x2 + 60x + -3600 = 0 Reorder the terms: -3600 + 60x + x2 = 0 Solving -3600 + 60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '3600' to each side of the equation. -3600 + 60x + 3600 + x2 = 0 + 3600 Reorder the terms: -3600 + 3600 + 60x + x2 = 0 + 3600 Combine like terms: -3600 + 3600 = 0 0 + 60x + x2 = 0 + 3600 60x + x2 = 0 + 3600 Combine like terms: 0 + 3600 = 3600 60x + x2 = 3600 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 = 3600 + 900 Reorder the terms: 900 + 60x + x2 = 3600 + 900 Combine like terms: 3600 + 900 = 4500 900 + 60x + x2 = 4500 Factor a perfect square on the left side: (x + 30)(x + 30) = 4500 Calculate the square root of the right side: 67.082039325 Break this problem into two subproblems by setting (x + 30) equal to 67.082039325 and -67.082039325.Subproblem 1
x + 30 = 67.082039325 Simplifying x + 30 = 67.082039325 Reorder the terms: 30 + x = 67.082039325 Solving 30 + x = 67.082039325 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 = 67.082039325 + -30 Combine like terms: 30 + -30 = 0 0 + x = 67.082039325 + -30 x = 67.082039325 + -30 Combine like terms: 67.082039325 + -30 = 37.082039325 x = 37.082039325 Simplifying x = 37.082039325Subproblem 2
x + 30 = -67.082039325 Simplifying x + 30 = -67.082039325 Reorder the terms: 30 + x = -67.082039325 Solving 30 + x = -67.082039325 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 = -67.082039325 + -30 Combine like terms: 30 + -30 = 0 0 + x = -67.082039325 + -30 x = -67.082039325 + -30 Combine like terms: -67.082039325 + -30 = -97.082039325 x = -97.082039325 Simplifying x = -97.082039325Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.082039325, -97.082039325}
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