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Simplifying x2 + -60x + -1700 = 0 Reorder the terms: -1700 + -60x + x2 = 0 Solving -1700 + -60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1700' to each side of the equation. -1700 + -60x + 1700 + x2 = 0 + 1700 Reorder the terms: -1700 + 1700 + -60x + x2 = 0 + 1700 Combine like terms: -1700 + 1700 = 0 0 + -60x + x2 = 0 + 1700 -60x + x2 = 0 + 1700 Combine like terms: 0 + 1700 = 1700 -60x + x2 = 1700 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 = 1700 + 900 Reorder the terms: 900 + -60x + x2 = 1700 + 900 Combine like terms: 1700 + 900 = 2600 900 + -60x + x2 = 2600 Factor a perfect square on the left side: (x + -30)(x + -30) = 2600 Calculate the square root of the right side: 50.990195136 Break this problem into two subproblems by setting (x + -30) equal to 50.990195136 and -50.990195136.Subproblem 1
x + -30 = 50.990195136 Simplifying x + -30 = 50.990195136 Reorder the terms: -30 + x = 50.990195136 Solving -30 + x = 50.990195136 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 = 50.990195136 + 30 Combine like terms: -30 + 30 = 0 0 + x = 50.990195136 + 30 x = 50.990195136 + 30 Combine like terms: 50.990195136 + 30 = 80.990195136 x = 80.990195136 Simplifying x = 80.990195136Subproblem 2
x + -30 = -50.990195136 Simplifying x + -30 = -50.990195136 Reorder the terms: -30 + x = -50.990195136 Solving -30 + x = -50.990195136 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 = -50.990195136 + 30 Combine like terms: -30 + 30 = 0 0 + x = -50.990195136 + 30 x = -50.990195136 + 30 Combine like terms: -50.990195136 + 30 = -20.990195136 x = -20.990195136 Simplifying x = -20.990195136Solution
The solution to the problem is based on the solutions from the subproblems. x = {80.990195136, -20.990195136}
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