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Simplifying x2 + 30x + -352 = 0 Reorder the terms: -352 + 30x + x2 = 0 Solving -352 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '352' to each side of the equation. -352 + 30x + 352 + x2 = 0 + 352 Reorder the terms: -352 + 352 + 30x + x2 = 0 + 352 Combine like terms: -352 + 352 = 0 0 + 30x + x2 = 0 + 352 30x + x2 = 0 + 352 Combine like terms: 0 + 352 = 352 30x + x2 = 352 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 = 352 + 225 Reorder the terms: 225 + 30x + x2 = 352 + 225 Combine like terms: 352 + 225 = 577 225 + 30x + x2 = 577 Factor a perfect square on the left side: (x + 15)(x + 15) = 577 Calculate the square root of the right side: 24.020824299 Break this problem into two subproblems by setting (x + 15) equal to 24.020824299 and -24.020824299.Subproblem 1
x + 15 = 24.020824299 Simplifying x + 15 = 24.020824299 Reorder the terms: 15 + x = 24.020824299 Solving 15 + x = 24.020824299 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 = 24.020824299 + -15 Combine like terms: 15 + -15 = 0 0 + x = 24.020824299 + -15 x = 24.020824299 + -15 Combine like terms: 24.020824299 + -15 = 9.020824299 x = 9.020824299 Simplifying x = 9.020824299Subproblem 2
x + 15 = -24.020824299 Simplifying x + 15 = -24.020824299 Reorder the terms: 15 + x = -24.020824299 Solving 15 + x = -24.020824299 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 = -24.020824299 + -15 Combine like terms: 15 + -15 = 0 0 + x = -24.020824299 + -15 x = -24.020824299 + -15 Combine like terms: -24.020824299 + -15 = -39.020824299 x = -39.020824299 Simplifying x = -39.020824299Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.020824299, -39.020824299}
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