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Simplifying x(x + 30) = 30 Reorder the terms: x(30 + x) = 30 (30 * x + x * x) = 30 (30x + x2) = 30 Solving 30x + x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + 30x + x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + 30x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 30x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 30x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 30x + x2 = 0 + 30 30x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 30x + x2 = 30 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 = 30 + 225 Reorder the terms: 225 + 30x + x2 = 30 + 225 Combine like terms: 30 + 225 = 255 225 + 30x + x2 = 255 Factor a perfect square on the left side: (x + 15)(x + 15) = 255 Calculate the square root of the right side: 15.968719423 Break this problem into two subproblems by setting (x + 15) equal to 15.968719423 and -15.968719423.Subproblem 1
x + 15 = 15.968719423 Simplifying x + 15 = 15.968719423 Reorder the terms: 15 + x = 15.968719423 Solving 15 + x = 15.968719423 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 = 15.968719423 + -15 Combine like terms: 15 + -15 = 0 0 + x = 15.968719423 + -15 x = 15.968719423 + -15 Combine like terms: 15.968719423 + -15 = 0.968719423 x = 0.968719423 Simplifying x = 0.968719423Subproblem 2
x + 15 = -15.968719423 Simplifying x + 15 = -15.968719423 Reorder the terms: 15 + x = -15.968719423 Solving 15 + x = -15.968719423 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 = -15.968719423 + -15 Combine like terms: 15 + -15 = 0 0 + x = -15.968719423 + -15 x = -15.968719423 + -15 Combine like terms: -15.968719423 + -15 = -30.968719423 x = -30.968719423 Simplifying x = -30.968719423Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.968719423, -30.968719423}
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