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Simplifying x(-1x + 63) = -2 Reorder the terms: x(63 + -1x) = -2 (63 * x + -1x * x) = -2 (63x + -1x2) = -2 Solving 63x + -1x2 = -2 Solving for variable 'x'. Reorder the terms: 2 + 63x + -1x2 = -2 + 2 Combine like terms: -2 + 2 = 0 2 + 63x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -63x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -63x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -63x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -63x + x2 = 0 + 2 -63x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -63x + x2 = 2 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 = 2 + 992.25 Reorder the terms: 992.25 + -63x + x2 = 2 + 992.25 Combine like terms: 2 + 992.25 = 994.25 992.25 + -63x + x2 = 994.25 Factor a perfect square on the left side: (x + -31.5)(x + -31.5) = 994.25 Calculate the square root of the right side: 31.531730051 Break this problem into two subproblems by setting (x + -31.5) equal to 31.531730051 and -31.531730051.Subproblem 1
x + -31.5 = 31.531730051 Simplifying x + -31.5 = 31.531730051 Reorder the terms: -31.5 + x = 31.531730051 Solving -31.5 + x = 31.531730051 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 = 31.531730051 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + x = 31.531730051 + 31.5 x = 31.531730051 + 31.5 Combine like terms: 31.531730051 + 31.5 = 63.031730051 x = 63.031730051 Simplifying x = 63.031730051Subproblem 2
x + -31.5 = -31.531730051 Simplifying x + -31.5 = -31.531730051 Reorder the terms: -31.5 + x = -31.531730051 Solving -31.5 + x = -31.531730051 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 = -31.531730051 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + x = -31.531730051 + 31.5 x = -31.531730051 + 31.5 Combine like terms: -31.531730051 + 31.5 = -0.031730051 x = -0.031730051 Simplifying x = -0.031730051Solution
The solution to the problem is based on the solutions from the subproblems. x = {63.031730051, -0.031730051}
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