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Simplifying x2 + 30x + 63 = 0 Reorder the terms: 63 + 30x + x2 = 0 Solving 63 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-63' to each side of the equation. 63 + 30x + -63 + x2 = 0 + -63 Reorder the terms: 63 + -63 + 30x + x2 = 0 + -63 Combine like terms: 63 + -63 = 0 0 + 30x + x2 = 0 + -63 30x + x2 = 0 + -63 Combine like terms: 0 + -63 = -63 30x + x2 = -63 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 = -63 + 225 Reorder the terms: 225 + 30x + x2 = -63 + 225 Combine like terms: -63 + 225 = 162 225 + 30x + x2 = 162 Factor a perfect square on the left side: (x + 15)(x + 15) = 162 Calculate the square root of the right side: 12.727922061 Break this problem into two subproblems by setting (x + 15) equal to 12.727922061 and -12.727922061.Subproblem 1
x + 15 = 12.727922061 Simplifying x + 15 = 12.727922061 Reorder the terms: 15 + x = 12.727922061 Solving 15 + x = 12.727922061 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 = 12.727922061 + -15 Combine like terms: 15 + -15 = 0 0 + x = 12.727922061 + -15 x = 12.727922061 + -15 Combine like terms: 12.727922061 + -15 = -2.272077939 x = -2.272077939 Simplifying x = -2.272077939Subproblem 2
x + 15 = -12.727922061 Simplifying x + 15 = -12.727922061 Reorder the terms: 15 + x = -12.727922061 Solving 15 + x = -12.727922061 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 = -12.727922061 + -15 Combine like terms: 15 + -15 = 0 0 + x = -12.727922061 + -15 x = -12.727922061 + -15 Combine like terms: -12.727922061 + -15 = -27.727922061 x = -27.727922061 Simplifying x = -27.727922061Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.272077939, -27.727922061}
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