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Simplifying x2 + 60x + -224 = 0 Reorder the terms: -224 + 60x + x2 = 0 Solving -224 + 60x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '224' to each side of the equation. -224 + 60x + 224 + x2 = 0 + 224 Reorder the terms: -224 + 224 + 60x + x2 = 0 + 224 Combine like terms: -224 + 224 = 0 0 + 60x + x2 = 0 + 224 60x + x2 = 0 + 224 Combine like terms: 0 + 224 = 224 60x + x2 = 224 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 = 224 + 900 Reorder the terms: 900 + 60x + x2 = 224 + 900 Combine like terms: 224 + 900 = 1124 900 + 60x + x2 = 1124 Factor a perfect square on the left side: (x + 30)(x + 30) = 1124 Calculate the square root of the right side: 33.526109228 Break this problem into two subproblems by setting (x + 30) equal to 33.526109228 and -33.526109228.Subproblem 1
x + 30 = 33.526109228 Simplifying x + 30 = 33.526109228 Reorder the terms: 30 + x = 33.526109228 Solving 30 + x = 33.526109228 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 = 33.526109228 + -30 Combine like terms: 30 + -30 = 0 0 + x = 33.526109228 + -30 x = 33.526109228 + -30 Combine like terms: 33.526109228 + -30 = 3.526109228 x = 3.526109228 Simplifying x = 3.526109228Subproblem 2
x + 30 = -33.526109228 Simplifying x + 30 = -33.526109228 Reorder the terms: 30 + x = -33.526109228 Solving 30 + x = -33.526109228 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 = -33.526109228 + -30 Combine like terms: 30 + -30 = 0 0 + x = -33.526109228 + -30 x = -33.526109228 + -30 Combine like terms: -33.526109228 + -30 = -63.526109228 x = -63.526109228 Simplifying x = -63.526109228Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.526109228, -63.526109228}
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