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Simplifying x2 + -60x + -2500 = 0 Reorder the terms: -2500 + -60x + x2 = 0 Solving -2500 + -60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '2500' to each side of the equation. -2500 + -60x + 2500 + x2 = 0 + 2500 Reorder the terms: -2500 + 2500 + -60x + x2 = 0 + 2500 Combine like terms: -2500 + 2500 = 0 0 + -60x + x2 = 0 + 2500 -60x + x2 = 0 + 2500 Combine like terms: 0 + 2500 = 2500 -60x + x2 = 2500 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 = 2500 + 900 Reorder the terms: 900 + -60x + x2 = 2500 + 900 Combine like terms: 2500 + 900 = 3400 900 + -60x + x2 = 3400 Factor a perfect square on the left side: (x + -30)(x + -30) = 3400 Calculate the square root of the right side: 58.309518948 Break this problem into two subproblems by setting (x + -30) equal to 58.309518948 and -58.309518948.Subproblem 1
x + -30 = 58.309518948 Simplifying x + -30 = 58.309518948 Reorder the terms: -30 + x = 58.309518948 Solving -30 + x = 58.309518948 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 = 58.309518948 + 30 Combine like terms: -30 + 30 = 0 0 + x = 58.309518948 + 30 x = 58.309518948 + 30 Combine like terms: 58.309518948 + 30 = 88.309518948 x = 88.309518948 Simplifying x = 88.309518948Subproblem 2
x + -30 = -58.309518948 Simplifying x + -30 = -58.309518948 Reorder the terms: -30 + x = -58.309518948 Solving -30 + x = -58.309518948 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 = -58.309518948 + 30 Combine like terms: -30 + 30 = 0 0 + x = -58.309518948 + 30 x = -58.309518948 + 30 Combine like terms: -58.309518948 + 30 = -28.309518948 x = -28.309518948 Simplifying x = -28.309518948Solution
The solution to the problem is based on the solutions from the subproblems. x = {88.309518948, -28.309518948}
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