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Simplifying x2 + 30x + 59 = 0 Reorder the terms: 59 + 30x + x2 = 0 Solving 59 + 30x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-59' to each side of the equation. 59 + 30x + -59 + x2 = 0 + -59 Reorder the terms: 59 + -59 + 30x + x2 = 0 + -59 Combine like terms: 59 + -59 = 0 0 + 30x + x2 = 0 + -59 30x + x2 = 0 + -59 Combine like terms: 0 + -59 = -59 30x + x2 = -59 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 = -59 + 225 Reorder the terms: 225 + 30x + x2 = -59 + 225 Combine like terms: -59 + 225 = 166 225 + 30x + x2 = 166 Factor a perfect square on the left side: (x + 15)(x + 15) = 166 Calculate the square root of the right side: 12.884098727 Break this problem into two subproblems by setting (x + 15) equal to 12.884098727 and -12.884098727.Subproblem 1
x + 15 = 12.884098727 Simplifying x + 15 = 12.884098727 Reorder the terms: 15 + x = 12.884098727 Solving 15 + x = 12.884098727 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 = 12.884098727 + -15 Combine like terms: 15 + -15 = 0 0 + x = 12.884098727 + -15 x = 12.884098727 + -15 Combine like terms: 12.884098727 + -15 = -2.115901273 x = -2.115901273 Simplifying x = -2.115901273Subproblem 2
x + 15 = -12.884098727 Simplifying x + 15 = -12.884098727 Reorder the terms: 15 + x = -12.884098727 Solving 15 + x = -12.884098727 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 = -12.884098727 + -15 Combine like terms: 15 + -15 = 0 0 + x = -12.884098727 + -15 x = -12.884098727 + -15 Combine like terms: -12.884098727 + -15 = -27.884098727 x = -27.884098727 Simplifying x = -27.884098727Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.115901273, -27.884098727}
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