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Simplifying x2 + 80x + -300 = 0 Reorder the terms: -300 + 80x + x2 = 0 Solving -300 + 80x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '300' to each side of the equation. -300 + 80x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + 80x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + 80x + x2 = 0 + 300 80x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 80x + x2 = 300 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 = 300 + 1600 Reorder the terms: 1600 + 80x + x2 = 300 + 1600 Combine like terms: 300 + 1600 = 1900 1600 + 80x + x2 = 1900 Factor a perfect square on the left side: (x + 40)(x + 40) = 1900 Calculate the square root of the right side: 43.588989435 Break this problem into two subproblems by setting (x + 40) equal to 43.588989435 and -43.588989435.Subproblem 1
x + 40 = 43.588989435 Simplifying x + 40 = 43.588989435 Reorder the terms: 40 + x = 43.588989435 Solving 40 + x = 43.588989435 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 = 43.588989435 + -40 Combine like terms: 40 + -40 = 0 0 + x = 43.588989435 + -40 x = 43.588989435 + -40 Combine like terms: 43.588989435 + -40 = 3.588989435 x = 3.588989435 Simplifying x = 3.588989435Subproblem 2
x + 40 = -43.588989435 Simplifying x + 40 = -43.588989435 Reorder the terms: 40 + x = -43.588989435 Solving 40 + x = -43.588989435 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 = -43.588989435 + -40 Combine like terms: 40 + -40 = 0 0 + x = -43.588989435 + -40 x = -43.588989435 + -40 Combine like terms: -43.588989435 + -40 = -83.588989435 x = -83.588989435 Simplifying x = -83.588989435Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.588989435, -83.588989435}
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