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Simplifying x2 + 60x + 36 = 0 Reorder the terms: 36 + 60x + x2 = 0 Solving 36 + 60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + 60x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + 60x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + 60x + x2 = 0 + -36 60x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 60x + x2 = -36 The x term is 60x. Take half its coefficient (30). Square it (900) and add it to both sides. Add '900' to each side of the equation. 60x + 900 + x2 = -36 + 900 Reorder the terms: 900 + 60x + x2 = -36 + 900 Combine like terms: -36 + 900 = 864 900 + 60x + x2 = 864 Factor a perfect square on the left side: (x + 30)(x + 30) = 864 Calculate the square root of the right side: 29.393876913 Break this problem into two subproblems by setting (x + 30) equal to 29.393876913 and -29.393876913.Subproblem 1
x + 30 = 29.393876913 Simplifying x + 30 = 29.393876913 Reorder the terms: 30 + x = 29.393876913 Solving 30 + x = 29.393876913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = 29.393876913 + -30 Combine like terms: 30 + -30 = 0 0 + x = 29.393876913 + -30 x = 29.393876913 + -30 Combine like terms: 29.393876913 + -30 = -0.606123087 x = -0.606123087 Simplifying x = -0.606123087Subproblem 2
x + 30 = -29.393876913 Simplifying x + 30 = -29.393876913 Reorder the terms: 30 + x = -29.393876913 Solving 30 + x = -29.393876913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + x = -29.393876913 + -30 Combine like terms: 30 + -30 = 0 0 + x = -29.393876913 + -30 x = -29.393876913 + -30 Combine like terms: -29.393876913 + -30 = -59.393876913 x = -59.393876913 Simplifying x = -59.393876913Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.606123087, -59.393876913}
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