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Simplifying x2 + 63x + -23 = 0 Reorder the terms: -23 + 63x + x2 = 0 Solving -23 + 63x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 63x + 23 + x2 = 0 + 23 Reorder the terms: -23 + 23 + 63x + x2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 63x + x2 = 0 + 23 63x + x2 = 0 + 23 Combine like terms: 0 + 23 = 23 63x + x2 = 23 The x term is 63x. Take half its coefficient (31.5). Square it (992.25) and add it to both sides. Add '992.25' to each side of the equation. 63x + 992.25 + x2 = 23 + 992.25 Reorder the terms: 992.25 + 63x + x2 = 23 + 992.25 Combine like terms: 23 + 992.25 = 1015.25 992.25 + 63x + x2 = 1015.25 Factor a perfect square on the left side: (x + 31.5)(x + 31.5) = 1015.25 Calculate the square root of the right side: 31.862987933 Break this problem into two subproblems by setting (x + 31.5) equal to 31.862987933 and -31.862987933.Subproblem 1
x + 31.5 = 31.862987933 Simplifying x + 31.5 = 31.862987933 Reorder the terms: 31.5 + x = 31.862987933 Solving 31.5 + x = 31.862987933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.5' to each side of the equation. 31.5 + -31.5 + x = 31.862987933 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + x = 31.862987933 + -31.5 x = 31.862987933 + -31.5 Combine like terms: 31.862987933 + -31.5 = 0.362987933 x = 0.362987933 Simplifying x = 0.362987933Subproblem 2
x + 31.5 = -31.862987933 Simplifying x + 31.5 = -31.862987933 Reorder the terms: 31.5 + x = -31.862987933 Solving 31.5 + x = -31.862987933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-31.5' to each side of the equation. 31.5 + -31.5 + x = -31.862987933 + -31.5 Combine like terms: 31.5 + -31.5 = 0.0 0.0 + x = -31.862987933 + -31.5 x = -31.862987933 + -31.5 Combine like terms: -31.862987933 + -31.5 = -63.362987933 x = -63.362987933 Simplifying x = -63.362987933Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.362987933, -63.362987933}
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