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Simplifying x2 + 30x + -75 = 0 Reorder the terms: -75 + 30x + x2 = 0 Solving -75 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '75' to each side of the equation. -75 + 30x + 75 + x2 = 0 + 75 Reorder the terms: -75 + 75 + 30x + x2 = 0 + 75 Combine like terms: -75 + 75 = 0 0 + 30x + x2 = 0 + 75 30x + x2 = 0 + 75 Combine like terms: 0 + 75 = 75 30x + x2 = 75 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 = 75 + 225 Reorder the terms: 225 + 30x + x2 = 75 + 225 Combine like terms: 75 + 225 = 300 225 + 30x + x2 = 300 Factor a perfect square on the left side: (x + 15)(x + 15) = 300 Calculate the square root of the right side: 17.320508076 Break this problem into two subproblems by setting (x + 15) equal to 17.320508076 and -17.320508076.Subproblem 1
x + 15 = 17.320508076 Simplifying x + 15 = 17.320508076 Reorder the terms: 15 + x = 17.320508076 Solving 15 + x = 17.320508076 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 = 17.320508076 + -15 Combine like terms: 15 + -15 = 0 0 + x = 17.320508076 + -15 x = 17.320508076 + -15 Combine like terms: 17.320508076 + -15 = 2.320508076 x = 2.320508076 Simplifying x = 2.320508076Subproblem 2
x + 15 = -17.320508076 Simplifying x + 15 = -17.320508076 Reorder the terms: 15 + x = -17.320508076 Solving 15 + x = -17.320508076 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 = -17.320508076 + -15 Combine like terms: 15 + -15 = 0 0 + x = -17.320508076 + -15 x = -17.320508076 + -15 Combine like terms: -17.320508076 + -15 = -32.320508076 x = -32.320508076 Simplifying x = -32.320508076Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.320508076, -32.320508076}
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