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Simplifying x2 + 80x + -1000 = 0 Reorder the terms: -1000 + 80x + x2 = 0 Solving -1000 + 80x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '1000' to each side of the equation. -1000 + 80x + 1000 + x2 = 0 + 1000 Reorder the terms: -1000 + 1000 + 80x + x2 = 0 + 1000 Combine like terms: -1000 + 1000 = 0 0 + 80x + x2 = 0 + 1000 80x + x2 = 0 + 1000 Combine like terms: 0 + 1000 = 1000 80x + x2 = 1000 The x term is 80x. Take half its coefficient (40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. 80x + 1600 + x2 = 1000 + 1600 Reorder the terms: 1600 + 80x + x2 = 1000 + 1600 Combine like terms: 1000 + 1600 = 2600 1600 + 80x + x2 = 2600 Factor a perfect square on the left side: (x + 40)(x + 40) = 2600 Calculate the square root of the right side: 50.990195136 Break this problem into two subproblems by setting (x + 40) equal to 50.990195136 and -50.990195136.Subproblem 1
x + 40 = 50.990195136 Simplifying x + 40 = 50.990195136 Reorder the terms: 40 + x = 50.990195136 Solving 40 + x = 50.990195136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = 50.990195136 + -40 Combine like terms: 40 + -40 = 0 0 + x = 50.990195136 + -40 x = 50.990195136 + -40 Combine like terms: 50.990195136 + -40 = 10.990195136 x = 10.990195136 Simplifying x = 10.990195136Subproblem 2
x + 40 = -50.990195136 Simplifying x + 40 = -50.990195136 Reorder the terms: 40 + x = -50.990195136 Solving 40 + x = -50.990195136 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + x = -50.990195136 + -40 Combine like terms: 40 + -40 = 0 0 + x = -50.990195136 + -40 x = -50.990195136 + -40 Combine like terms: -50.990195136 + -40 = -90.990195136 x = -90.990195136 Simplifying x = -90.990195136Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.990195136, -90.990195136}
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