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Simplifying x2 + 30x + 80 = 0 Reorder the terms: 80 + 30x + x2 = 0 Solving 80 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-80' to each side of the equation. 80 + 30x + -80 + x2 = 0 + -80 Reorder the terms: 80 + -80 + 30x + x2 = 0 + -80 Combine like terms: 80 + -80 = 0 0 + 30x + x2 = 0 + -80 30x + x2 = 0 + -80 Combine like terms: 0 + -80 = -80 30x + x2 = -80 The x term is 30x. Take half its coefficient (15). Square it (225) and add it to both sides. Add '225' to each side of the equation. 30x + 225 + x2 = -80 + 225 Reorder the terms: 225 + 30x + x2 = -80 + 225 Combine like terms: -80 + 225 = 145 225 + 30x + x2 = 145 Factor a perfect square on the left side: (x + 15)(x + 15) = 145 Calculate the square root of the right side: 12.041594579 Break this problem into two subproblems by setting (x + 15) equal to 12.041594579 and -12.041594579.Subproblem 1
x + 15 = 12.041594579 Simplifying x + 15 = 12.041594579 Reorder the terms: 15 + x = 12.041594579 Solving 15 + x = 12.041594579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = 12.041594579 + -15 Combine like terms: 15 + -15 = 0 0 + x = 12.041594579 + -15 x = 12.041594579 + -15 Combine like terms: 12.041594579 + -15 = -2.958405421 x = -2.958405421 Simplifying x = -2.958405421Subproblem 2
x + 15 = -12.041594579 Simplifying x + 15 = -12.041594579 Reorder the terms: 15 + x = -12.041594579 Solving 15 + x = -12.041594579 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-15' to each side of the equation. 15 + -15 + x = -12.041594579 + -15 Combine like terms: 15 + -15 = 0 0 + x = -12.041594579 + -15 x = -12.041594579 + -15 Combine like terms: -12.041594579 + -15 = -27.041594579 x = -27.041594579 Simplifying x = -27.041594579Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.958405421, -27.041594579}
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